Question 1

Champa bought some pants and skirts at a sale. If the number of skirts is two less than twice the number of pants, and also four less than four times the number of pants, how many pants did she buy?

Accepted Answer

Correct Option: A. Solution: Let $x$ be the number of pants and $y$ be the number of skirts. The equations are $y = 2x - 2$ and $y = 4x - 4$. Setting these equal gives $2x - 2 = 4x - 4$, which simplifies to $x = 1$. Therefore, she bought 1 pant.

Question 2

What is the solution for $x$ in the system of equations $x + 2y = 3$ and $7x - 15y = 2$ using substitution?

Accepted Answer

Correct Option: A. Solution: After finding $y = \frac{19}{29}$, substitute back into $x = 3 - 2y$ to get $x = \frac{49}{29}$.

Question 3

If two linear equations are given by $5x - 8y + 1 = 0$ and $3x - \frac{24}{5}y + \frac{3}{5} = 0$, what can be said about their solutions?

Accepted Answer

Correct Option: C. Solution: Multiplying the second equation by 5/3 gives the same equation as the first, indicating coincident lines with infinitely many solutions.

Question 4

Given the equations $$2x + 3y = 7$$ and $$4x + 6y = 14$$, what can be inferred about their graphical representation?

Accepted Answer

Correct Option: C. Solution: The second equation is a multiple of the first, indicating that the lines are coincident. Thus, they have infinitely many solutions.

Question 5

Using the substitution method, solve the equations $7x - 15y = 2$ and $x + 2y = 3$. What is the value of $x$?

Accepted Answer

Correct Option: A. Solution: Substitute $x = 3 - 2y$ into $7x - 15y = 2$ to find $y = \frac{19}{29}$, then $x = \frac{49}{29}$.

Question 6

Meena went to a bank to withdraw ₹2000. She received ₹50 and ₹100 notes, totaling 25 notes. How many ₹100 notes did she receive?

Accepted Answer

Correct Option: B. Solution: Let $x$ be the number of ₹50 notes and $y$ be the number of ₹100 notes. The equations are $x + y = 25$ and $50x + 100y = 2000$. Solving these gives $x = 15$ and $y = 10$. Therefore, she received 10 ₹100 notes.

Question 7

What is the first step in the elimination method for solving a pair of linear equations?

Accepted Answer

Correct Option: A. Solution: The elimination method involves multiplying the equations by suitable constants to make the coefficients of one variable equal, allowing for elimination.

Question 8

For the pair of equations $$x + 3y = 6$$ and $$2x - 3y = 12$$, what is the solution when solved using the substitution method?

Accepted Answer

Correct Option: B. Solution: Substitute $y = \frac{6 - x}{3}$ from the first equation into the second: $$2x - 3\left(\frac{6 - x}{3}\right) = 12$$. Simplifying gives $x = 6$ and $y = 0$.

Question 9

Which of the following conditions indicates that a pair of linear equations has no solution when represented graphically?

Accepted Answer

Correct Option: B. Solution: When the lines are parallel, they do not intersect, indicating that the pair of linear equations has no solution.

Question 10

Consider the pair of linear equations: $$3x + 4y = 20$$ and $$6x + 8y = 40$$. Determine the nature of the system of equations.

Accepted Answer

Correct Option: C. Solution: The equations are multiples of each other, i.e., $$6x + 8y = 40$$ is twice $$3x + 4y = 20$$, indicating they are coincident lines. Thus, the system is consistent with infinitely many solutions.

Question 11

What is the first step in the elimination method when solving the pair of equations $$3x + 2y = 5$$ and $$6x + 4y = 10$$?

Accepted Answer

Correct Option: B. Solution: To eliminate a variable, we first make the coefficients of one of the variables equal by multiplying the equations appropriately.

Question 12

In the elimination method, if after eliminating a variable, the resulting equation is a false statement like $0 = 9$, what does this imply about the pair of linear equations?

Accepted Answer

Correct Option: D. Solution: A false statement implies that the pair of equations is inconsistent and has no solution.

Question 13

Consider the pair of linear equations: $$x + 2y - 4 = 0$$ and $$2x + 4y - 12 = 0$$. What is the nature of the solution for this pair of equations?

Accepted Answer

Correct Option: B. Solution: The equations represent parallel lines because their ratios $$\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$$, indicating no solution.

Question 14

Which of the following pairs of linear equations has a unique solution?

Accepted Answer

Correct Option: D. Solution: The equations $x + 3y = 6$ and $2x - 3y = 12$ intersect at a single point, indicating a unique solution.

Question 15

Champa bought some pants and skirts. If the number of skirts is two less than twice the number of pants, and also four less than four times the number of pants, how many pants did she buy?

Accepted Answer

Correct Option: A. Solution: Let the number of pants be $x$ and skirts be $y$. The equations are $y = 2x - 2$ and $y = 4x - 4$. Solving these gives $x = 1$ pant.

Question 16

For the pair of equations $x + 2y = 4$ and $2x + 4y = 8$, what is the nature of their graphical representation?

Accepted Answer

Correct Option: C. Solution: The equations $x + 2y = 4$ and $2x + 4y = 8$ represent coincident lines because they are multiples of each other, indicating infinitely many solutions.

Question 17

Using the substitution method, solve the system of equations: $$5x - 8y + 1 = 0$$ and $$3x - \frac{24}{5}y + \frac{3}{5} = 0$$. What is the nature of the solution?

Accepted Answer

Correct Option: B. Solution: Both equations simplify to the same line, indicating that they are coincident, thus having infinitely many solutions.

Question 18

In the elimination method, if the resulting equation after elimination is $$0 = 0$$, what does it imply about the system of equations?

Accepted Answer

Correct Option: C. Solution: The equation $$0 = 0$$ indicates that the system of equations is dependent and consistent, leading to infinitely many solutions.

Question 19

Using the elimination method, solve the pair of equations: $$2x - 3y = 4$$ and $$4x - 6y = 8$$. What is the nature of the solution?

Accepted Answer

Correct Option: C. Solution: Both equations are equivalent, hence they have infinitely many solutions.

Question 20

Given the equations $x + 2y = 3$ and $7x - 15y = 2$, what is the value of $y$ when using the substitution method?

Accepted Answer

Correct Option: A. Solution: Using the substitution method, $x$ is expressed as $x = 3 - 2y$ and substituted into the second equation to solve for $y = \frac{19}{29}$.

Question 21

Given the equations $$x + 2y = 3$$ and $$7x - 15y = 2$$, which step correctly represents the substitution method to solve for $y$?

Accepted Answer

Correct Option: A. Solution: Using the substitution method, solve for $x$ in the first equation: $x = 3 - 2y$. Substitute this expression for $x$ into the second equation to solve for $y$.

Question 22

Which of the following statements is true about the substitution method?

Accepted Answer

Correct Option: B. Solution: The substitution method involves expressing one variable in terms of another and substituting it into the other equation.

Question 23

A pair of linear equations is given by $$3x + 4y = 10$$ and $$6x + 8y = 20$$. Determine the nature of their graphical representation.

Accepted Answer

Correct Option: C. Solution: The equations represent coincident lines because they are scalar multiples of each other, indicating infinitely many solutions.

Question 24

In a city, the taxi fare consists of a fixed charge plus a charge per kilometer. For a 10 km journey, the fare is ₹105, and for a 15 km journey, it is ₹155. What is the charge per kilometer?

Accepted Answer

Correct Option: B. Solution: Let $f$ be the fixed charge and $c$ be the charge per kilometer. The equations are $f + 10c = 105$ and $f + 15c = 155$. Subtracting these gives $5c = 50$, so $c = 10$. Therefore, the charge per kilometer is ₹10.

Question 25

Which of the following pairs of equations represent lines that are parallel?

Accepted Answer

Correct Option: D. Solution: The equations $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$ have the same slope but different intercepts, indicating parallel lines.

Question 26

For the pair of equations $$x + 2y = 5$$ and $$2x + 4y = 10$$, determine the relationship between the coefficients and the nature of the solutions.

Accepted Answer

Correct Option: B. Solution: The equations are proportional, $$\frac{1}{2} = \frac{2}{4} = \frac{5}{10}$$, indicating that the lines are coincident and the system is consistent with infinitely many solutions.

Question 27

If the lines represented by two linear equations are coincident, what can be said about the system of equations?

Accepted Answer

Correct Option: C. Solution: When lines are coincident, the system of equations has infinitely many solutions, as every point on the line is a solution.

Question 28

For the equations $2x + 3y = 8$ and $4x + 6y = 7$, what can be concluded if the elimination method leads to $0 = 9$?

Accepted Answer

Correct Option: B. Solution: The elimination method leading to $0 = 9$ indicates that the equations are inconsistent and have no solution.

Question 29

Which of the following pairs of equations represents a consistent pair of linear equations?

Accepted Answer

Correct Option: B. Solution: Option b represents intersecting lines, hence a consistent pair with a unique solution.

Question 30

Akhila went to a fair and spent ₹20 on rides and games. If each ride on the Giant Wheel costs ₹3 and each game of Hoopla costs ₹4, and the number of Hoopla games is half the number of rides, how many rides did she take?

Accepted Answer

Correct Option: B. Solution: Let the number of rides be $x$ and the number of Hoopla games be $y$. We have $y = \frac{1}{2}x$ and $3x + 4y = 20$. Solving these, $x = 3$ rides.

Question 31

In the elimination method, if after eliminating one variable, you obtain a true statement like $18 = 18$, what does this indicate?

Accepted Answer

Correct Option: C. Solution: A true statement like $18 = 18$ indicates that the system of equations has infinitely many solutions.

Question 32

Akhila went to a fair and spent ₹20 on rides and games. If the number of games she played is half the number of rides she took, and each ride costs ₹3 while each game costs ₹4, how many rides did she take?

Accepted Answer

Correct Option: B. Solution: Let the number of rides be $x$ and the number of games be $y$. We have $y = \frac{1}{2}x$ and $3x + 4y = 20$. Solving these equations, we get $x = 3$ and $y = 1.5$. Since $y$ must be an integer, $x = 3$ is the only valid solution.

Question 33

Consider the pair of linear equations: $$x + 2y - 4 = 0$$ and $$2x + 4y - 12 = 0$$. What is the nature of the solution for this pair of equations?

Accepted Answer

Correct Option: B. Solution: The given equations are parallel lines since their slopes are equal and the constant terms differ, indicating no points of intersection. Thus, they have no solution.

Question 34

Which condition indicates that a pair of linear equations is inconsistent?

Accepted Answer

Correct Option: C. Solution: The condition $\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$ indicates that the lines are parallel, hence the equations are inconsistent.

Question 35

In a shop, the cost of 2 pencils and 3 erasers is ₹9, and the cost of 4 pencils and 6 erasers is ₹18. What can you conclude about the system of equations representing this situation?

Accepted Answer

Correct Option: C. Solution: The equations $2x + 3y = 9$ and $4x + 6y = 18$ are equivalent, meaning they represent the same line. Therefore, the system has infinitely many solutions.

Question 36

In the elimination method, if after eliminating one variable, you obtain a false statement like $0 = 9$, what does this indicate about the system of equations?

Accepted Answer

Correct Option: B. Solution: A false statement like $0 = 9$ indicates that the system of equations is inconsistent and has no solution.

Question 37

If the pair of linear equations $$x + 2y = 8$$ and $$2x + 4y = 16$$ are solved using the elimination method, what will be the result?

Accepted Answer

Correct Option: C. Solution: Both equations represent the same line, hence they have infinitely many solutions.

Question 38

Given the equations $9x - 4y = 2000$ and $7x - 3y = 2000$, what is the next step after making the coefficients of $y$ equal?

Accepted Answer

Correct Option: B. Solution: After making the coefficients of $y$ equal, subtract one equation from the other to eliminate $y$ and solve for $x$.

Question 39

Consider the system of equations: $$3x + 4y = 20$$ and $$y = \frac{1}{2}x$$. Using the substitution method, find the value of $x$.

Accepted Answer

Correct Option: C. Solution: Substitute $y = \frac{1}{2}x$ into the first equation: $$3x + 4\left(\frac{1}{2}x\right) = 20$$, which simplifies to $$3x + 2x = 20$$ or $$5x = 20$$. Solving for $x$ gives $x = 4$.

Question 40

In the substitution method for solving the pair of linear equations, which step involves substituting the expression of one variable into the other equation?

Accepted Answer

Correct Option: B. Solution: In the substitution method, Step 2 involves substituting the expression of one variable into the other equation to solve for the remaining variable.

Question 41

Two rails are represented by the equations $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$. Will the rails cross each other?

Accepted Answer

Correct Option: B. Solution: The equations $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$ are parallel lines, as they have the same slope but different intercepts. Hence, they do not intersect.

Question 42

Consider the pair of linear equations: $$3x + 4y = 20$$ and $$6x + 8y = 40$$. What can be concluded about the nature of these equations?

Accepted Answer

Correct Option: C. Solution: The given equations are multiples of each other, hence they are dependent and have infinitely many solutions.

Question 43

Analyze the system of equations $$5x - 4y = 8$$ and $$10x - 8y = 18$$. What conclusion can be drawn about the system?

Accepted Answer

Correct Option: B. Solution: The equations are not proportional, $$\frac{5}{10} = \frac{4}{8} 
eq \frac{8}{18}$$, indicating that the lines are parallel and the system is inconsistent with no solution.

Question 44

Akhila went to a fair and spent a total of ₹20 on rides and Hoopla games. If the cost of each ride on the Giant Wheel is ₹3 and each game of Hoopla costs ₹4, and the number of Hoopla games she played is half the number of rides she took, how many rides did she take?

Accepted Answer

Correct Option: A. Solution: Let $x$ be the number of rides and $y$ be the number of Hoopla games. Given $y = \frac{1}{2}x$ and $3x + 4y = 20$. Substituting $y = \frac{1}{2}x$ into the second equation gives $3x + 4(\frac{1}{2}x) = 20$, simplifying to $5x = 20$, so $x = 4$. However, this solution does not satisfy the budget constraint. Re-evaluating the setup, $y = \frac{1}{2}x$ implies $x = 2$ for the budget to be satisfied.

Question 45

In the substitution method, if after substitution the resulting equation is a false statement, the pair of linear equations is consistent.

Accepted Answer

Answer: False. Solution: A false statement after substitution indicates that the pair of linear equations is inconsistent and has no solutions.

Question 46

The elimination method involves making the coefficients of one variable equal by multiplying the equations by suitable constants.

Accepted Answer

Answer: True. Solution: In the elimination method, we multiply the equations by suitable constants to make the coefficients of one variable equal, allowing us to eliminate that variable.

Question 47

The substitution method involves expressing one variable in terms of another and substituting it into the second equation.

Accepted Answer

Answer: True. Solution: In the substitution method, one variable is expressed in terms of the other and substituted into the second equation to solve the pair of linear equations.

Question 48

The equations $2x + 3y = 9$ and $4x + 6y = 18$ have infinitely many solutions.

Accepted Answer

Answer: True. Solution: The equations $2x + 3y = 9$ and $4x + 6y = 18$ are equivalent, meaning they represent the same line, thus having infinitely many solutions.

Question 49

If the coefficients of a pair of linear equations satisfy $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$, the equations are inconsistent.

Accepted Answer

Answer: False. Solution: If $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$, the equations are dependent and consistent, having infinitely many solutions.

Question 50

The elimination method can be used to solve a pair of linear equations even if they are inconsistent.

Accepted Answer

Answer: False. Solution: If a pair of linear equations is inconsistent, it means they have no solution. The elimination method cannot find a solution in such a case.

Question 51

For a pair of linear equations given by $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$, if $\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$, the system is inconsistent.

Accepted Answer

Answer: True. Solution: When $\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$, the lines are parallel, indicating an inconsistent system with no solutions.

Question 52

The substitution method involves expressing one variable in terms of the other and substituting it into the second equation.

Accepted Answer

Answer: True. Solution: In the substitution method, one variable is expressed in terms of the other from one equation and substituted into the second equation to solve for the variables.

Question 53

A pair of linear equations is considered inconsistent if the lines representing them are parallel.

Accepted Answer

Answer: True. Solution: If the lines are parallel, the pair of linear equations has no solution and is thus inconsistent.

Question 54

If the pair of linear equations $x + 2y = 4$ and $2x + 4y = 8$ are graphed, they will intersect at a single point.

Accepted Answer

Answer: False. Solution: The equations $x + 2y = 4$ and $2x + 4y = 8$ represent the same line, hence they are coincident and have infinitely many solutions.

Question 55

The substitution method is the most convenient method for solving pairs of linear equations when the solution has non-integral coordinates.

Accepted Answer

Answer: True. Solution: The substitution method is preferred over the graphical method when solutions have non-integral coordinates, as it avoids potential reading errors.

Question 56

If two linear equations in two variables are represented by lines that coincide, the pair of equations has infinitely many solutions.

Accepted Answer

Answer: True. Solution: When two lines coincide, every point on the line is a solution, resulting in infinitely many solutions. This is a dependent and consistent pair of equations.

Question 57

A pair of linear equations in two variables that are parallel have no solution.

Accepted Answer

Answer: True. Solution: Parallel lines represent an inconsistent pair of linear equations, meaning they do not intersect and thus have no solution.

Question 58

A pair of linear equations with parallel lines has a unique solution.

Accepted Answer

Answer: False. Solution: Parallel lines never intersect, meaning the pair of equations has no solution, making it inconsistent.

Question 59

Using the substitution method, if the resulting equation after substitution is a true statement without variables, the pair of linear equations has infinitely many solutions.

Accepted Answer

Answer: True. Solution: If substituting one variable into the other equation results in a true statement with no variables, it indicates that the equations are dependent and have infinitely many solutions.

Question 60

The substitution method involves solving one of the linear equations for one variable and substituting this expression into the other equation.

Accepted Answer

Answer: True. Solution: The substitution method requires expressing one variable in terms of the other from one equation and substituting it into the second equation to solve for the remaining variable.

Question 61

If the substitution method results in a false statement, the pair of linear equations is inconsistent.

Accepted Answer

Answer: True. Solution: A false statement after substitution indicates that the pair of linear equations has no solution and is inconsistent.

Question 62

If the elimination method results in a true statement with no variables, the pair of equations has infinitely many solutions.

Accepted Answer

Answer: True. Solution: When the elimination method results in a true statement with no variables, it indicates that the original pair of equations has infinitely many solutions.

Question 63

In the elimination method, if subtracting the equations results in a false statement like $0 = 9$, the pair of equations has no solution.

Accepted Answer

Answer: True. Solution: A false statement such as $0 = 9$ indicates that the pair of equations is inconsistent and has no solution.

Question 64

Parallel lines representing a pair of linear equations indicate that the system is consistent.

Accepted Answer

Answer: False. Solution: Parallel lines indicate that the system has no solutions, making it inconsistent.

Pair of Linear Equations ..

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Graphical Solution of Linear Equations

Algebraic Methods of Solving Linear Equations

Conditions for Consistency of Linear Equations

Application of Linear Equations in Real-Life Problems

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Graphical Solution of Linear Equations

Algebraic Methods of Solving Linear Equations

Conditions for Consistency of Linear Equations

Application of Linear Equations in Real-Life Problems

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Multiple Choice Questions

Q1.Champa bought some pants and skirts at a sale. If the number of skirts is two less than twice the number of pants, and also four less than four times the number of pants, how many pants did she buy?

Correct Answer: A

Q2.What is the solution for xxx in the system of equations x+2y=3x + 2y = 3x+2y=3 and 7x−15y=27x - 15y = 27x−15y=2 using substitution?

Correct Answer: A

Q3.If two linear equations are given by 5x−8y+1=05x - 8y + 1 = 05x−8y+1=0 and 3x−245y+35=03x - \frac{24}{5}y + \frac{3}{5} = 03x−524​y+53​=0, what can be said about their solutions?

Correct Answer: C

Q4.Given the equations 2x+3y=72x + 3y = 72x+3y=7 and 4x+6y=144x + 6y = 144x+6y=14, what can be inferred about their graphical representation?

Correct Answer: C

Q5.Using the substitution method, solve the equations 7x−15y=27x - 15y = 27x−15y=2 and x+2y=3x + 2y = 3x+2y=3. What is the value of xxx?

Correct Answer: A

Q6.Meena went to a bank to withdraw ₹2000. She received ₹50 and ₹100 notes, totaling 25 notes. How many ₹100 notes did she receive?

Correct Answer: B

Q7.What is the first step in the elimination method for solving a pair of linear equations?

Correct Answer: A

Q8.For the pair of equations x+3y=6x + 3y = 6x+3y=6 and 2x−3y=122x - 3y = 122x−3y=12, what is the solution when solved using the substitution method?

Correct Answer: B

Q9.Which of the following conditions indicates that a pair of linear equations has no solution when represented graphically?

Correct Answer: B

Q10.Consider the pair of linear equations: 3x+4y=203x + 4y = 203x+4y=20 and 6x+8y=406x + 8y = 406x+8y=40. Determine the nature of the system of equations.

Correct Answer: C

Q11.What is the first step in the elimination method when solving the pair of equations 3x+2y=53x + 2y = 53x+2y=5 and 6x+4y=106x + 4y = 106x+4y=10?

Correct Answer: B

Q12.In the elimination method, if after eliminating a variable, the resulting equation is a false statement like 0=90 = 90=9, what does this imply about the pair of linear equations?

Correct Answer: D

Q13.Consider the pair of linear equations: x+2y−4=0x + 2y - 4 = 0x+2y−4=0 and 2x+4y−12=02x + 4y - 12 = 02x+4y−12=0. What is the nature of the solution for this pair of equations?

Correct Answer: B

Q14.Which of the following pairs of linear equations has a unique solution?

Correct Answer: D

Q15.Champa bought some pants and skirts. If the number of skirts is two less than twice the number of pants, and also four less than four times the number of pants, how many pants did she buy?

Correct Answer: A

Q16.For the pair of equations x+2y=4x + 2y = 4x+2y=4 and 2x+4y=82x + 4y = 82x+4y=8, what is the nature of their graphical representation?

Correct Answer: C

Q17.Using the substitution method, solve the system of equations: 5x−8y+1=05x - 8y + 1 = 05x−8y+1=0 and 3x−245y+35=03x - \frac{24}{5}y + \frac{3}{5} = 03x−524​y+53​=0. What is the nature of the solution?

Correct Answer: B

Q18.In the elimination method, if the resulting equation after elimination is 0=00 = 00=0, what does it imply about the system of equations?

Correct Answer: C

Q19.Using the elimination method, solve the pair of equations: 2x−3y=42x - 3y = 42x−3y=4 and 4x−6y=84x - 6y = 84x−6y=8. What is the nature of the solution?

Correct Answer: C

Q20.Given the equations x+2y=3x + 2y = 3x+2y=3 and 7x−15y=27x - 15y = 27x−15y=2, what is the value of yyy when using the substitution method?

Correct Answer: A

Q21.Given the equations x+2y=3x + 2y = 3x+2y=3 and 7x−15y=27x - 15y = 27x−15y=2, which step correctly represents the substitution method to solve for yyy?

Correct Answer: A

Q22.Which of the following statements is true about the substitution method?

Correct Answer: B

Q23.A pair of linear equations is given by 3x+4y=103x + 4y = 103x+4y=10 and 6x+8y=206x + 8y = 206x+8y=20. Determine the nature of their graphical representation.

Correct Answer: C

Q24.In a city, the taxi fare consists of a fixed charge plus a charge per kilometer. For a 10 km journey, the fare is ₹105, and for a 15 km journey, it is ₹155. What is the charge per kilometer?

Correct Answer: B

Q25.Which of the following pairs of equations represent lines that are parallel?

Correct Answer: D

Q26.For the pair of equations x+2y=5x + 2y = 5x+2y=5 and 2x+4y=102x + 4y = 102x+4y=10, determine the relationship between the coefficients and the nature of the solutions.

Correct Answer: B

Q27.If the lines represented by two linear equations are coincident, what can be said about the system of equations?

Correct Answer: C

Q28.For the equations 2x+3y=82x + 3y = 82x+3y=8 and 4x+6y=74x + 6y = 74x+6y=7, what can be concluded if the elimination method leads to 0=90 = 90=9?

Correct Answer: B

Q29.Which of the following pairs of equations represents a consistent pair of linear equations?