Class 9 Maths Linear Equation in Two Variables MCQs with Answer

Class 9 Maths Linear Equations in Two Variables MCQs

Linear Equations in Two Variables is an important chapter in Class 9 Maths because it helps students understand how mathematical equations are represented through graphs and coordinates. This chapter builds a strong connection between algebra and coordinate geometry. This section on Class 9 Maths Linear Equations in Two Variables MCQs with Answer is designed to help students practice important concepts in a simple and clear way based on the latest CBSE syllabus.

The linear equations in two variables class 9 mcq set includes questions on equations with two variables, solutions of linear equations, plotting points on graphs, and identifying coordinates correctly. Students can also practice class 9 maths chapter 4 mcq with answers to improve conceptual understanding and problem-solving skills step by step. Regular practice of linear equations in two variables mcq class 9 helps students reduce calculation mistakes and improve confidence in graph-based questions.

In addition, students can attempt a class 9 maths chapter 4 mcq online test to improve speed and accuracy. These MCQs are based on important concepts like Cartesian plane, ordered pairs, graph plotting, and finding solutions of equations. Many students understand equations but become confused while plotting graphs or finding correct coordinate points. That is why regular practice becomes very important for scoring better marks in exams.

What is Linear Equations in Two Variables MCQ Class 9?

Linear Equations in Two Variables MCQs for Class 9 Maths are multiple-choice questions that test a student’s understanding of equations involving two variables and their graphical representation. These questions are an important part of Class 9 Maths Chapter 4 MCQs with answers and help students prepare effectively for exams.

In these questions, students learn about variables, linear equations, solutions of equations, coordinate points, and plotting graphs on the Cartesian plane. They also practice finding whether a point satisfies a given equation or not.

Regular practice of linear equations in two variables mcq class 9 improves graph understanding, accuracy, and confidence. It also helps students perform better in CBSE school exams and online tests.

Important Terms in Linear Equations in Two Variables

This table is very useful for solving class 9 maths chapter 4 mcq online test questions quickly and accurately.

Important Tricks for Linear Equations in Two Variables MCQs (Class 9)

Here are some simple tricks used in linear equations in two variables class 9 mcq questions:

Check the Degree Carefully:
A linear equation always has degree 1.

Verify the Solution:
Put the values of x and y into the equation to check whether both sides are equal or not.

Understand Ordered Pairs Properly:
The first value represents x-coordinate and the second value represents y-coordinate.

Graph Representation:
The graph of a linear equation in two variables is always a straight line.

These tricks are very helpful in solving class 9 maths linear equations in two variables MCQs with answers.

Q. Which of the following equations represents a linear equation in two variables?

1. x² + 3y = 5 
2. 2x − 7y = 0 
3. x + y² = 9
4. xy = 4 

Answer: B

Explanation:

A linear equation in two variables is an equation that can be written in the form Ax + By + C = 0, where A, B, and C are real numbers, and A and B are not both zero. In a linear equation, the highest power of each variable is 1. Option (a) x² + 3y = 5 is not linear because x has a power of 2, while option (c) x + y² = 9 is not linear because y has a power of 2. Option (d) xy = 4 is also not linear because it contains the product of two variables, x and y. Only option (b) 2x − 7y = 0 satisfies the definition of a linear equation in two variables.

Q. How many solutions does a linear equation in two variables typically have?

1. Exactly one solution
2. Exactly two solutions
3. No solution
4. Infinitely many solutions

Answer: D

Explanation:

A linear equation in two variables, such as Ax + By + C = 0, represents a straight line when graphed on a Cartesian plane. Every point (x, y) that lies on this line is a solution to the equation. Since a straight line extends infinitely in both directions and contains infinitely many points, a single linear equation in two variables has infinitely many solutions.

Q. Which of the following points is a solution to the equation 3x − 2y = 6?

1. (0, 3)
2. (2, 0)
3. (1, 1)
4. (4, 2)

Answer: D

Explanation:

To determine whether a point (x, y) is a solution to the equation 3x − 2y = 6, substitute the values of x and y into the equation and check if the equality is satisfied. For (0, 3): 3(0) − 2(3) = 0 − 6 = −6, which is not equal to 6, so it is not a solution. For (2, 0): 3(2) − 2(0) = 6 − 0 = 6, which satisfies the equation, so it is a solution. For (1, 1): 3(1) − 2(1) = 3 − 2 = 1, which is not equal to 6, so it is not a solution. For (4, 2): 3(4) − 2(2) = 12 − 4 = 8, which is not equal to 6, so it is not a solution. Therefore, only (2, 0) is a solution to the equation 3x − 2y = 6.

Q. If the point (3, k) is a solution to the equation 4x − 3y = 9, what is the value of k?

1. 1
2. -1
3. 2
4. -2

Answer: A

Explanation:

Given that the point (3, k) is a solution to the equation 4x − 3y = 9, substitute x = 3 and y = k into the equation: 4(3) − 3(k) = 9. Simplifying gives 12 − 3k = 9. Subtract 12 from both sides to get −3k = −3. Dividing both sides by −3 gives k = 1. Therefore, the value of k is 1.

Q. Which of the following equations represents a line parallel to the x-axis?

1. x = 5
2. y = −3
3. x + y = 0
4. 2x − y = 1

Answer: B

Explanation:

A line parallel to the x-axis has a constant y-coordinate for all points on the line, while the x-coordinate can vary. The equation of such a line is always of the form y = c, where c is a constant. Option (a) x = 5 represents a vertical line parallel to the y-axis. Option (b) y = −3 represents a horizontal line where the y-coordinate always remains −3, making it parallel to the x-axis. Option (c) x + y = 0 represents a slanted line passing through the origin. Option (d) 2x − y = 1 also represents a slanted line. Therefore, y = −3 is the equation of a line parallel to the x-axis.

Q. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. Let the cost of a notebook be x and the cost of a pen be y. 

1. x = y + 2
2. y = 2x
3. x = 2y
4. x + y = 2

Answer: C

Explanation:

Let x be the cost of a notebook and y be the cost of a pen. The statement “The cost of a notebook is twice the cost of a pen” can be written mathematically as:

Cost of notebook = 2 × (Cost of pen)

Therefore, x = 2y. This can also be written as x − 2y = 0, which is a linear equation in two variables.

Q. Which of the following is NOT a linear equation in two variables?

1. 5x − 0y = 10
2. 0x + 7y = 14
3. x + 1/y = 3
4. x − y = 0

Answer: C

Explanation:

A linear equation in two variables can be written in the form Ax + By + C = 0, where A, B, and C are real numbers, and A and B are not both zero. The variables x and y must have powers equal to 1. Option (a) 5x − 0y = 10 can be written as 5x + 0y − 10 = 0, which is a linear equation. Option (b) 0x + 7y = 14 can be written as 0x + 7y − 14 = 0, which is also a linear equation. Option (d) x − y = 0 is already in the standard form of a linear equation. However, option (c) x + 1/y = 3 can be written as x + y⁻¹ = 3, where the power of y is −1 instead of 1. Therefore, x + 1/y = 3 is not a linear equation in two variables.

Q. If (a, 4) is a solution of the equation 3x + y = 10, then the value of a is:

1. 1
2. 2
3. 3
4. 4

Answer: B

Explanation:

Given that the point (a, 4) is a solution to the equation 3x + y = 10, substitute x = a and y = 4 into the equation. This gives 3(a) + 4 = 10. Subtracting 4 from both sides, we get 3a = 6. Dividing both sides by 3 gives a = 2. Therefore, the value of a is 2.

Q. The graph of the equation y = 3x passes through which of the following points?

1. (1, 3)
2. (3, 1)
3. (0, 3)
4. (3, 0)

Answer: A

Explanation:

A point (x, y) lies on the graph of an equation if its coordinates satisfy the equation. To determine which point lies on the graph of y = 3x, substitute the coordinates of each point into the equation. For (1, 3): 3 = 3(1), which is true, so (1, 3) lies on the graph. For (3, 1): 1 = 3(3), which is false. For (0, 3): 3 = 3(0), which is false. For (3, 0): 0 = 3(3), which is also false. Therefore, the graph of the equation y = 3x passes through the point (1, 3).

Q. Express the equation 5x = −y + 8 in the standard form Ax + By + C = 0.

1. 5x + y − 8 = 0
2. 5x − y + 8 = 0
3. 5x + y + 8 = 0
4. 5x − y − 8 = 0 

Answer: A

Explanation:

The standard form of a linear equation in two variables is Ax + By + C = 0, where A, B, and C are real numbers, and A and B are not both zero. Given the equation 5x = −y + 8, move all the terms to one side of the equation. Adding y to both sides gives 5x + y = 8. Subtracting 8 from both sides gives 5x + y − 8 = 0. Therefore, the standard form of the equation is 5x + y − 8 = 0.

Q. A linear equation in two variables has a unique solution when:

1. It is represented by a single equation.
2. It is part of a system of two intersecting lines.
3. It is part of a system of two parallel lines.
4. It is part of a system of two coincident lines.

Answer: B

Explanation:

A single linear equation in two variables, such as ax + by = c, represents a straight line and has infinitely many solutions because every point on the line satisfies the equation. A unique solution is possible only when two linear equations are considered together as a system. If the two lines intersect at exactly one point, the system has a unique solution, which is the point of intersection. If the lines are parallel, they never intersect and therefore have no solution. If the lines are coincident, they overlap completely and have infinitely many solutions. Thus, a unique solution exists when two linear equations form intersecting lines.

Q. The equation x = 0 represents which of the following?

1. The x-axis
2. The y-axis
3. A line parallel to the x-axis
4. A line parallel to the y-axis

Answer: B

Explanation:

In a Cartesian coordinate system, the x-axis is the horizontal line where the y-coordinate of every point is 0, so its equation is y = 0. The y-axis is the vertical line where the x-coordinate of every point is 0, so its equation is x = 0. Therefore, the equation x = 0 represents the y-axis.

Q. For the equation 2x + 3y = 12, if y = 0, what is the value of x?

1. 4
2. 6
3. 0
4. 2

Answer: B

Explanation:

Given the equation 2x + 3y = 12, we need to find the value of x when y = 0. Substitute y = 0 into the equation: 2x + 3(0) = 12. This simplifies to 2x = 12. Dividing both sides by 2 gives x = 6. Therefore, when y = 0, the value of x is 6, and the line intersects the x-axis at the point (6, 0).

Q. If x = 2 and y = 1 is a solution to the equation ax − 3y = 7, then the value of a is:

1. 2
2. 3
3. 4
4. 5

Answer: D

Explanation:

Given that x = 2 and y = 1 is a solution to the equation ax − 3y = 7, substitute the values x = 2 and y = 1 into the equation. This gives a(2) − 3(1) = 7. Simplifying, we get 2a − 3 = 7. Add 3 to both sides to obtain 2a = 10. Dividing both sides by 2 gives a = 5. Therefore, the value of a is 5.

Q. Which of the following lines passes through the origin (0, 0)?

1. x + y = 5
2. 2x − y = 0
3. y = x + 1
4. x = 3

Answer: B

Explanation:

A line passes through the origin (0, 0) if the coordinates x = 0 and y = 0 satisfy its equation. Substitute these values into each option. For (a) x + y = 5: 0 + 0 = 0, which is not equal to 5, so the line does not pass through the origin. For (b) 2x − y = 0: 2(0) − 0 = 0, which satisfies the equation, so the line passes through the origin. For (c) y = x + 1: 0 = 0 + 1, which is false. For (d) x = 3: 0 = 3, which is also false. Therefore, the equation 2x − y = 0 represents a line passing through the origin.

Q. Which of the following is a solution to the equation x - 4y = 8?

1. (0, 2)
2. (4, 1)
3. (8, 0)
4. (1, -4)

Answer: C

Explanation:

To determine which point is a solution to the equation x − 4y = 8, substitute the values of x and y from each option into the equation. For (0, 2): 0 − 4(2) = 0 − 8 = −8, which is not equal to 8, so it is not a solution. For (4, 1): 4 − 4(1) = 4 − 4 = 0, which is not equal to 8, so it is not a solution. For (8, 0): 8 − 4(0) = 8 − 0 = 8, which satisfies the equation, so it is a solution. For (1, −4): 1 − 4(−4) = 1 + 16 = 17, which is not equal to 8, so it is not a solution. Therefore, (8, 0) is a solution to the equation x − 4y = 8.

Q. The graph of y = mx passes through the origin. If it also passes through the point (2, 6), what is the value of m?

1. 2
2. 3
3. 4
4. 6

Answer: B

Explanation:

Given the equation y = mx, the graph passes through the point (2, 6). This means that when x = 2, y = 6. Substitute these values into the equation: 6 = m(2). Simplifying gives 6 = 2m. Dividing both sides by 2, we get m = 3. Therefore, the value of m is 3.

Q. Which of the following statements is true for the equation x + y = 7?

1. It has exactly one solution.
2. It has exactly two solutions.
3. It has no solution.
4. It has infinitely many solutions.

Answer: D

Explanation:

A linear equation in two variables, such as x + y = 7, represents a straight line on a coordinate plane. Every point (x, y) lying on this line satisfies the equation and is therefore a solution. Since a straight line extends infinitely in both directions and contains infinitely many points, a linear equation in two variables has infinitely many solutions.

Q. The graph of the linear equation 2x + y = k passes through the point (1, 3). Find the value of k.

1. 4
2. 5
3. 6
4. 7

Answer: B

Explanation: 

Given that the graph of the linear equation 2x + y = k passes through the point (1, 3), the coordinates x = 1 and y = 3 satisfy the equation. Substitute these values into the equation: 2(1) + 3 = k. Simplifying gives 2 + 3 = k, so k = 5. Therefore, the value of k is 5.

Q. Which of the following ordered pairs is a solution to the equation y = 1/2 x − 2?

1. (4, 0)
2. (0, 2)
3. (2, 1)
4. (-2, -1)

Answer: A

Explanation:

To determine which ordered pair is a solution to the equation y = 1/2 x − 2, substitute the values of x and y from each option into the equation and check whether both sides are equal. For (4, 0): 0 = 1/2(4) − 2 = 2 − 2 = 0, which is true, so (4, 0) is a solution. For (0, 2): 2 = 1/2(0) − 2 = 0 − 2 = −2, which is false. For (2, 1): 1 = 1/2(2) − 2 = 1 − 2 = −1, which is false. For (−2, −1): −1 = 1/2(−2) − 2 = −1 − 2 = −3, which is also false. Therefore, (4, 0) is the solution to the equation.

Q. If the sum of two numbers is 15, and one number is x and the other is y, which equation represents this relationship?

1. x − y = 15
2. xy = 15
3. x + y = 15
4. x/y = 15

Answer: C

Explanation:

The problem states that the sum of two numbers is 15. Let the two numbers be x and y. Since “sum” means addition, we add x and y and set the result equal to 15. Therefore, the equation representing this relationship is x + y = 15. 

Q. The equation of a line parallel to the y-axis at a distance of 4 units to the right of it is:

1. x = 4
2. x = -4
3. y = 4
4. y = -4

Answer: A

Explanation:

A line parallel to the y-axis is a vertical line, and every point on a vertical line has the same x-coordinate. The y-axis itself is represented by the equation x = 0. If a line is parallel to the y-axis and located 4 units to the right of it, then the x-coordinate of every point on the line is 4. Therefore, the equation of the line is x = 4.

Q. Which of the following represents the graph of y = 0?

1. The x-axis
2. The y-axis
3. A line parallel to the x-axis, not passing through the origin
4. A line passing through the origin with a positive slope

Answer: A

Explanation:

In a Cartesian coordinate system, the x-axis is the horizontal line where the y-coordinate of every point is 0, so its equation is y = 0. The y-axis is the vertical line where the x-coordinate of every point is 0, so its equation is x = 0. Therefore, the equation y = 0 represents the x-axis.

Q. The point where the graph of 2x - 5y = 10 intersects the y-axis is:

1. (0, -2)
2. (5, 0)
3. (0, 2)
4. (-2, 0)

Answer: A

Explanation:

The y-axis is defined by the equation x = 0. To find the point where the graph of 2x − 5y = 10 intersects the y-axis, substitute x = 0 into the equation and solve for y. This gives 2(0) − 5y = 10, which simplifies to −5y = 10. Dividing both sides by −5, we get y = −2. Therefore, the graph intersects the y-axis at the point (0, −2).

Q. If the graph of a linear equation in two variables is a horizontal line, then its equation is of the form:

1. x = a
2. y = a
3. x + y = a
4. y = ax

Answer: B

Explanation:

A horizontal line is a line parallel to the x-axis. For every point on a horizontal line, the y-coordinate remains constant regardless of the x-coordinate. Therefore, the equation of a horizontal line is always of the form y = a, where a is a constant. In contrast, x = a represents a vertical line, x + y = a represents a slant line with slope −1, and y = ax represents a line passing through the origin with slope a.

Q. The point (-3, -4) lies in which quadrant?

1. First Quadrant
2. Second Quadrant
3. Third Quadrant
4. Fourth Quadrant

Answer: C

Explanation:

The Cartesian plane is divided into four quadrants based on the signs of the x- and y-coordinates. In the First Quadrant, both x and y are positive. In the Second Quadrant, x is negative and y is positive. In the Third Quadrant, both x and y are negative. In the Fourth Quadrant, x is positive and y is negative. The point (−3, −4) has a negative x-coordinate and a negative y-coordinate, so it lies in the Third Quadrant.

Q. Which of the following is an equation of a line passing through the point (0, -4) and parallel to the x-axis?

1. x = -4
2. y = -4
3. x + y = -4
4. y = 4x

Answer: B

Explanation:

A line parallel to the x-axis is a horizontal line, and the equation of any horizontal line is of the form y = c, where c is a constant. Since the line passes through the point (0, −4), the y-coordinate is always −4. Therefore, the value of c is −4, and the equation of the line is y = −4.

Q. The Equation Ax + By + C = 0 is a linear equation in two variables if:

1. A = 0 and B = 0 
2. A ≠ 0 or B ≠ 0 
3. A = 0 and C = 0
4. B = 0 and C = 0

Answer: B

Explanation:

The standard form of a linear equation in two variables is Ax + By + C = 0. For it to represent a linear equation in two variables, at least one of the coefficients A or B must be non-zero. If both A and B are zero, the equation reduces to C = 0, which does not involve the variables x and y. Therefore, the required condition is A ≠ 0 or B ≠ 0. 

Q. The point of intersection of the lines x = 5 and y = −2 is:

1. (5, 2)
2. (-5, 2)
3. (5, -2)
4. (-5, -2)

Answer: C

Explanation:

The point of intersection of two lines is the point (x, y) that satisfies both equations simultaneously. From the equations x = 5 and y = −2, we directly get the x-coordinate as 5 and the y-coordinate as −2. Therefore, the point of intersection is (5, −2). 

Q. Which of the following equations represents a line passing through the point (2, -1) with a slope of 3?

1. y = 3x − 7
2. y = 3x + 5
3. y = 3x − 1
4. y = −3x + 5

Answer: A

Explanation:

We need to find the equation of a line passing through the point (2, −1) with slope m = 3. Using the point-slope form of a line, y − y₁ = m(x − x₁), substitute the values x₁ = 2, y₁ = −1, and m = 3:

y − (−1) = 3(x − 2)

Simplifying gives:

y + 1 = 3x − 6

Subtract 1 from both sides:

y = 3x − 7

Checking the options, y = 3x − 7 satisfies both the given slope and the point (2, −1). Therefore, the correct equation is y = 3x − 7.

Linear Equations in Two Variables MCQ Preparation Tips

Follow these simple tips to score better:

Practice solving equations regularly

Learn graph plotting carefully on graph paper

Understand how ordered pairs work in equations

Revise coordinate geometry basics properly

Solve linear equations in two variables mcq class 9 online tests regularly

Use NCERT and CBSE-based questions for better preparation

Conclusion

Practicing Class 9 Maths Linear Equations in Two Variables MCQs with answers is one of the best ways to improve algebraic and graph-based problem-solving skills. It helps students understand equations more clearly and improves confidence in solving coordinate-related questions.

Regular practice also helps students reduce mistakes while plotting graphs, identifying solutions, and solving equation-based MCQs in school exams and online tests.