Chapter Test Pair of Linear Equation in Two Variables CBSE ICSE

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25 Question MCQ Prime Maths - Class X, IX CBSE, Madhyamik and ICSE

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Pair of Linear Equations in Two Variables

This quiz offers a thorough evaluation of key concepts and skills related to Linear Equations in Two Variables, encompassing 25 multiple-choice questions designed to test both theoretical understanding and practical application for CBSE, Madhyamik and ICSE students of classes IX and X. It explores the conditions for unique, infinite, or no solutions and their graphical interpretations—parallel, intersecting, or coincident lines. Through computational problems, students solve for unknown constants and variables using algebraic methods like substitution and elimination, while applied word problems connect the topic to real-world contexts such as age puzzles, digit problems, taxi fares, and boat stream challenges. Ideal for high school learners, this assessment reinforces core algebraic reasoning and problem-solving techniques, providing a solid foundation for further mathematical studies and competitive exam preparation in a structured, engaging format.

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📝 Instructions

• This quiz contains 25 multiple choice questions.
• Select only one correct answer per question.
• Use the navigator to jump between questions.
• Submit when you are finished to see results.

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Question 1

For the system of equations \(a_1x + b_1y + c_1 = 0\) and \(a_2x + b_2y + c_2 = 0\) to have a unique solution, the condition is:

A\(\frac{a_1}{a_2} = \frac{b_1}{b_2}\) B\(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\) C\(\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\) D\(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)

Question 2

If a pair of linear equations is consistent, then the lines representing them are:

AParallel BAlways coincident CIntersecting or coincident DAlways intersecting

Question 3

For what value of \(k\) do the equations \(3x - y + 8 = 0\) and \(6x - ky = -16\) represent coincident lines?

A\(k = 2\) B\(k = -2\) C\(k = \frac{1}{2}\) D\(k = - \frac{1}{2}\)

Question 4

The pair of equations \(x = a\) and \(y = b\) graphically represents lines which are:

AParallel BIntersecting at \((b, a)\) CCoincident DIntersecting at \((a, b)\)

Question 5

If the system \(2x + 3y = 5\) and \(4x + ky = 10\) has infinitely many solutions, then \(k\) equals:

A\(1\) B\(\frac{3}{2}\) C\(6\) D\(3\)

Question 6

The value of \(k\) for which the system \(x + 2y = 3\) and \(5x + ky + 7 = 0\) is inconsistent is:

A\(k = 10\) B\(k = \frac{2}{5}\) C\(k = -\frac{2}{5}\) D\(k = -10\)

Question 7

Solve: \(\frac{x}{a}+\frac{y}{b}=2\) and \(ax-by=a^2-b^2\)

A\(x=a, \quad y=b^2\) B\(x=a, \quad y=b\) C\(x=a^2, \quad y=b^2\) D\(x=a^2, \quad y=b\)

Question 8

The value of \(k\) for which the pair of linear equations \((3k+1)x+3y=2\) and \((k^2+1)x+(k-2)y-5=0\) has no solution.

A\(k=-2\) B\(k=2\) C\(k=1\) D\(k=-1\)

Question 9

Solve for \(x\) and \(y\): \((a-b)x + (a+b)y = a^2 -2ab-b^2\) and \((a+b)(x+y) = a^2 + b^2\)

A\(x = a+b, y = -\frac{2ab}{a+b}\) B\(x = a+b, y = \frac{2ab}{a+b}\) C\(x = a-b, y = -\frac{2ab}{a+b}\) D\(x = a-b, y = \frac{2ab}{a+b}\)

Question 10

The value of \(x\) satisfying \(\frac{5}{x-1}+\frac{1}{y-2}=2\) and \(\frac{6}{x-1}-\frac{3}{y-2}-1=0, \quad x \neq 1, y \neq 2\) is:

A2 B3 C4 D5

Question 11

If \(37x + 43y = 123\) and \(43x + 37y = 117\), then:

A\(x = 2, y = 3\) B\(x = 1, y = 2\) C\(x = 3, y = 2\) D\(x = -1, y = -2\)

Question 12

The pair of equations \(225x + 881y = 2^{10}\) and \(450x + 1762y = 2048\) has:

ANo solution BUnique solution CTwo solutions DInfinitely many solutions

Question 13

If \(\frac{b}{a}x + \frac{a}{b}y = a^2+b^2\) and \(x + y = 2ab\) then

A\(x=2y\) B\(x=-y\) C\(x=y\) D\(2x=y\)

Question 14

If \(2^x + 3^y = 17\) and \(2^{x+2} - 3^{y+1} = 5\), find \(x\) and \(y\).

A\(x = 9, y = 5\) B\(x = 3, y = 2\) C\(x = 5, y = 9\) D\(x = 8, y = 6\)

Question 15

Solve for \(x\): \(\frac{2}{x} + \frac{3}{y} = 13\) and \(\frac{5}{x} - \frac{4}{y} = -2\).

A\(x = 1/2\) B\(x = 1/3\) C\(x = 2\) D\(x = 3\)

Question 16

For what value of \(p\) does the pair of equations \(4x + py + 8 = 0\) and \(2x + 2y + 2 = 0\) have a unique solution?

A\(p = 4\) B\(p \neq 4\) C\(p = 2\) D\(p \neq 2\)

Question 17

If \(49x + 51y = 499\) and \(51x + 49y = 501\), then \(x\) is:

A3 B5.5 C4 D6.5

Question 18

The difference between two numbers is 26 and one number is three times the other. Find them.

A30, 4 B36, 10 C39, 13 D40, 14

Question 19

Solve: \( \sqrt{2}x + \sqrt{3}y = 0 \) and \( \sqrt{3}x - \sqrt{8}y = 0 \).

A\(x=1, y=1\) B\(x=\sqrt{2}, y=\sqrt{3}\) C\(x=0, y=0\) D\(x=2, y=3\)

Question 20

Find \(k\) if the lines \(x + 2y - 1 = 0\) and \(2x + ky + 2 = 0\) are parallel.

A\(k=2\) B\(k=3\) C\(k=4\) D\(k=-4\)

Question 21

Five years ago, Ramesh was thrice as old as Sonu. Ten years later, Ramesh will be twice as old as Sonu. What is Ramesh's present age?

A40 years B50 years C60 years D45 years

Question 22

A fraction becomes 9/11 if 2 is added to both numerator and denominator. If 3 is added to both, it becomes 5/6. Find the fraction.

A\(7/9\) B\(9/7\) C\(5/9\) D\(3/7\)

Question 23

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

A18 B27 C81 D72

Question 24

A taxi charge consists of a fixed charge together with the charge for the distance covered. For 10 km, the charge paid is ₹105 and for 15 km, the charge paid is ₹155. What are the fixed charges?

A₹ 10 B₹ 5 C₹ 15 D₹ 8

Question 25

Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water.

A6 km/h B4 km/h C8 km/h D10 km/h

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