Mock Test - Linear Equations in Two Variables

Class 9 Mathematics – Chapter 4: Linear Equations in Two Variables (MCQ Mock Test)

Strengthen Your Algebra Skills with the Linear Equations MCQ Mock Test!

Can you represent equations graphically or find their solutions easily? Test your understanding with this MCQ-based mock test on Linear Equations in Two Variables, designed as per the latest Class 9 Maths syllabus. This test includes all important concepts — standard form of linear equations, plotting their graphs, finding solutions, and interpreting parallel and intersecting lines.

Each question helps you apply mathematical reasoning, enhance visualization skills, and gain confidence for exams. Whether you’re preparing for school tests or revising for finals, this mock test is the perfect way to build a strong foundation for algebra and coordinate geometry.

Attempt now and make solving Linear Equations in Two Variables simpler than ever!

1. The linear equation 3y – 5 = 0, represented as ax + by + c = 0, h

a unique solution

infinitely many solutions

two solutions

no solution

2. Find b, if linear equation 3bx – y = 9 has one solution as (3, 3).

1/3

2/3

4/3

Zero

3. Any point on the line y = x is of the form

(a, a)

(0, a)

(a, 0)

(a, – a)

4. The equation x = 5 in two variables can be written as

1.x + 1.y = 5

0.x + 1.y = 5

0.x + 0.y = 5

1.x + 0.y = 5

5. Any solution of the linear equation 2x + 0y = 9 in two variables, is of the form

(a)

(b)

(c)

(d)

6. If the linear equation has solutions (– 3, 3), (0, 0), (3, – 3), then equation is

x – y = 0

x + y = 0

2x – y = 0

x + 2y = 0

7. Assertion (A): x + y = 6 is the equation of a line passing through the origin.
Reason (R): y = mx is the equation of a line passing through the origin.

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Assertion (A) is true but reason (R) is false.

Assertion (A) is false but reason (R) is true.

8. For one of the solutions of the equation ax + by + c = 0, x is negative and y is positive then surely a portion of line lies in the

first quadrant

second quadrant

third quadrant

fourth quadrant

9. At what point the graph of the linear equation 2x + 5y = 10 cuts the y-axis?

(0,1)

(0,2)

(0,3)

(0,4)

10. How many solution(s) of the linear equation 2x + 3y = 18 has?

One

Two

Infinite

Three

11. The graph of the linear equation y = 2x passes through the point

(2, 1)

(2, – 1)

12.

If (2, 0) is a solution of the linear equation 2x + 3y = k, then find the value of k.

13. For what value of k, x = 2 and y = –1 is a solution of x + 3y – k = 0.

-1

14. Side of an equilateral triangle is x. If the perimeter is 30 cm, find the value of x.

15. Assertion (A): A linear equation 3x + 5y =2 has infinitely many solutions.
Reason (R): A linear equation in two variables has many infinitely solutions.

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Assertion (A) is true but reason (R) is false.

Assertion (A) is false but reason (R) is true.

16. If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:

changes

remains the same

changes in case of multiplication only

changes in case of division only.

17. If point (3, 0) lies on the graph of the equation 2x + 3y = k, then the value of k is

18. Find the value of b, if x = 5, y = 0 is a solution of the equation 3x + 5y = b.

19. How many linear equations in x and y can be satisfied by x = 1 and y = 2?

Only one

Two

Infinitely many

Three

20. Assertion (A): There are infinite number of lines passing through (2, 5).
Reason (R): A linear equation in two variables has unique solution.

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Assertion (A) is true but reason (R) is false.

Assertion (A) is false but reason (R) is true.

21. The equation of x-axis is of the form

x = 0

y = 0

x + y = 0

x = y

22. The solution of the linear equation x + 2y = 8 which represents a point on x-axis is (0, 4).

True

False

23. Let y varies directly as x. If y = 24, when x = 8, then the linear equation is

3y = x

y = x

y = 4x

y = 3x

24. The graph of the linear equation 3x + 5y = 15 cuts the x-axis at the point

(5, 0)

(3, 0)

(0, 5)

(0, 3)

25. The equation x = 5 in two variables can be written as

1.x + 1.y = 5

0.x + 1.y = 5

0.x + 0.y = 5

1.x + 0.y = 5

26. x = 5, y = –2 is a solution of the linear equation

2x + y = 9

2x – y = 12

x + 3y = 1

x + 3y = 0

27. The graph of x = ± a is a straight line parallel to the

x-axis

y-axis

line y = x

line x + y = 0

28. Assertion (A): x = 4 is a line parallel to x-axis.
Reason (R): The equation of the line parallel to the y-axis is x = a.

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Assertion (A) is true but reason (R) is false.

Assertion (A) is false but reason (R) is true.

29. The equation 2x + 5y = 7 has a unique solution, if x, y are

Natural numbers

Positive real numbers

Real numbers

Rational numbers

30. A linear equation in two variables is of the form ax + by + c = 0, where

a ≠ 0, b ≠ 0

a = 0, b ≠ 0

a ≠ 0, b = 0

a = 0, c = 0

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