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MCQ Questions of Linear Equations in Two Variables with Answers

Review the Class 9 Maths MCQ Questions of Linear Equations in Two Variables with Answers below. MCQ Questions for Class 9 Maths with Answers are created based on the latest pattern of the exams. We provide linear equations in two-variable, Class Math 10 multiple choice answers, help students to understand the concept well.

Students can also refer to NCERT’s class 9 two-variable mathematical linear equation solutions to better prepare for the exam. The MCQ questions for higher marks are put forward here. so that students can get good marks. Provide these objective questions online, and provide detailed answers and explanations.

MCQ Questions for class 9, Linear equations in two variables are given below: –

1. The linear equation 3x-11y=10 has:

(a) Unique solution
(b) Two solutions
(c) Infinitely many solutions
(d) No solutions

2. The linear equation 4x – 10y = 14 has:

(a) A unique solution
(b) Two solutions
(c) Infinitely many solutions
(d) No solutions

3. 3x+10 = 0 will has:

(a) Unique solution
(b) Two solutions
(c) Infinitely many solutions
(d) No solutions

4. The solution of equation x-2y = 4 is:

(a) (0,2)
(b) (2,0)
(c) (4,0)
(d) (1,1)

5. Find the value of k, if x = 1, y = 2 is a solution of the equation 2x + 3y = k.

(a) 5
(b) 6
(c) 7
(d) 8

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

(a) 4
(b) 6
(c) 5
(d) 2

7. The graph of the linear equation 2x +3y = 6 cuts the y-axis at the point:

(a) (2, 0)
(b) (0, 3)
(c) (3, 0)
(d) (0, 2)

8. The equation y = 5, in two variables, can be written as:

(a) 1 .x + 1 .y = 5
(b) 0 .x + 0 .y = 5
(c) 1 .x + 0 .y = 5
(d) 0 .x + 1 .y = 5

9. Point (3, 4) lies on the graph of the equation 3y = kx + 7. The value of k is:

(a) 4/3
(b) 5/3
(c) 3
(d) 7/3

10. The graph of linear equation x+2y = 2, cuts the y-axis at:

(a) (2,0)
(b) (0,2)
(c) (0,1)
(d) (1,1)

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

(a) (a, –a)
(b) (0, a)
(c) (a, 0)
(d) (a, a)

12. The graph of x = 5 is a line:

(a) Parallel to x-axis at a distance 5 units from the origin
(b) Parallel to y-axis at a distance 5 units from the origin
(c) Making an intercept 5 on the x-axis
(d) Making an intercept 5 on the y-axis

13. In equation, y = mx+c, m is:

(a) Intercept
(b) Slope of the line
(c) Solution of the equation
(d) None of the above

14. If x and y are both positive solutions of equation ax+by+c=0, always lie in:

(a) First quadrant
(b) Second quadrant
(c) Third quadrant
(d) Fourth quadrant

15. Any point on the x-axis is of the form:

(a) (0, y)
(b) (x, 0)
(c) (x, x)
(d) (x, y)

16. The positive solutions of the equation ax + by + c = 0 always lie in the:

(a) 1st quadrant
(b) 2nd quadrant
(c) 3rd quadrant
(d) 4th quadrant

17. The point of the form (a, –a) always lies on the line:

(a) x = a
(b) y = –a
(c) y = x
(d) x + y = 0

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

(a) Remains the same
(b) Changes
(c) Changes in case of multiplication only
(d) Changes in case of division only

19. The point of the form (a, a) always lies on:

(a) On the line x + y = 0
(b) On the line y = x
(c) x-axis
(d) y-axis

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

(a) Rational numbers
(b) Real numbers
(c) Natural numbers
(d) Positive real numbers

Answers & Explanations

1. Answer: (c) Infinitely many solutions
Explanation: 3x-11y=10

y=(10-3x)/11

Now for infinite values of x, y will also have the infinite solutions.

2. Answer: (c) Infinitely many solutions

3. Answer: (a) Unique solution
Explanation: 3x+10 = 0

x = -10/3.

Hence, only one solution is possible.

4. Answer: (c) (4,0)

Explanation: Putting x=4 and y = 0, on the L.H.S. of the given equation, we get;

4-2(0) = 4 – 0 = 4

Which is equal to R.H.S.

5. Answer: (d) 8

Explanation: 2x + 3y = k

k=2(1)+3(2) = 2+6 = 8

6. Answer: (a) 4

7. Answer: (d) (0, 2)

8. Answer: (d) 0 .x + 1 .y = 5

9. Answer: (b) 5/3

Explanation: 3y = kx + 7

Here, x = 3 and y = 4

Hence,

(3×4) = (kx3) + 7

12 = 3k+7

3k = 12–7

3k = 5

k = 5/3

10. Answer: (c) (0,1)

Explanation: x+2y = 2

y = (2-x)/2

If x=0, then;

y=(2-0)/2 = 2/2 = 1

Hence, x+2y=2 cuts the y-axis at (0,1).

11. Answer: (d) (a, a)

12. Answer: (b) Parallel to y-axis at a distance 5 units from the origin

13. Answer: (b) Slope of the line

14. Answer: (a) First quadrant

15. Answer: (b) (x, 0)

16. Answer: (a) 1st quadrant

17. Answer: (d) x + y = 0

18. Answer: (a) Remains the same

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

19. Answer: (b) On the line y = x

Explanation: The point of the form (a, a) always lies on the line y = x. If the point having the same x and y values, it should lie on the same line.

20. Answer: (c) Natural numbers

Explanation: The equation 2x + 5y = 7 has a unique solution, if x, y are natural numbers.

In natural numbers, there exists only one pair (1, 1) which satisfies the given equation. But for rational numbers, real numbers, positive real numbers, there exist many solution pairs to satisfy the equation.

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