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SparkEd Math offers 60+ practice questions for Linear Equations in Two Variables across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

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SparkEd Math uses visual step-by-step solutions for every Linear Equations in Two Variables problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Linear Equations in Two Variables content aligned with the CBSE syllabus?

Yes, all Linear Equations in Two Variables questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Linear Equations in Two Variables — Class 9 CBSE (2025-26)

About Linear Equations in Two Variables — Class 9 CBSE

Form and graph linear equations in two variables; find solutions as ordered pairs. This topic is part of the CBSE Class 9 mathematics syllabus (chapter: Chapter 4). On this page you can practice 63 questions across three difficulty levels — 22 easy, 20 medium, and 21 hard — each with a visual step-by-step solution, plus a timed 36-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Linear Equations in Two Variables

Introduction to Linear Equations in Two Variables
Understanding Solutions of Linear Equations
Graphing Linear Equations
Special Cases: Equations of Lines Parallel to Axes
Summary, Connections, and Practice

Interactive lesson · about 15 minutes · checkpoint question after every unit

Linear Equations in Two Variables — solved examples for Class 9 CBSE

Example 1easy

Which of the following is a linear equation in two variables?

A)2x + 3y = 5
B)x² + y = 7
C)xy = 4
D)3x = 9

Step-by-step solution

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 degree of each variable (x and y) must be 1. Option A, 2x + 3y = 5 (or 2x + 3y - 5 = 0), fits this definition as both x and y have a degree of 1.
Options B (x² + y = 7) has x with degree 2, option C (xy = 4) has a product of variables making it non-linear, and option D (3x = 9) is a linear equation in only one variable.

Answer: 2x + 3y = 5

Example 2medium

Express the linear equation 3x = 5y - 7 in the standard form ax + by + c = 0 and identify the values of a, b, and c.

A)a=3, b=5, c=7
B)a=3, b=-5, c=7
C)a=3, b=-5, c=-7
D)a=3, b=5, c=-7

Step-by-step solution

The given equation is 3x = 5y - 7.
To express it in the standard form ax + by + c = 0, move all terms to the left-hand side.
Subtract 5y from both sides and add 7 to both sides: 3x - 5y + 7 = 0.
Comparing this with ax + by + c = 0, we get a = 3, b = -5, and c = 7.

Answer: a=3, b=-5, c=7

Example 3hard

The graph of the linear equation (p-1)x + (2p+1)y = 10 passes through the point (2, 2). What is the value of 'p'?

A)-5/3
B)1
C)5/3
D)2

Step-by-step solution

Substitute the coordinates of the point (2, 2) into the given equation (p-1)x + (2p+1)y = 10.
This gives: (p-1)(2) + (2p+1)(2) = 10.
Expand and simplify the equation: 2p - 2 + 4p + 2 = 10, which simplifies to 6p = 10.
Solve for 'p': p = 10/6 = 5/3.

Answer: 5/3

Practice questions on Linear Equations in Two Variables

Q1.easy
Express the equation 3x = 5y - 8 in the standard form ax + by + c = 0 and identify the value of 'c'.
1. A)c = 8
2. B)c = -8
3. C)c = 3
4. D)c = -5
Show answer
Answer: c = 8
Hint: Rearrange the terms to bring all of them to one side of the equation, ensuring the constant term is isolated.
Q2.easy
Which of the following points is a solution to the equation 2x + y = 7?
1. A)(1, 4)
2. B)(3, 2)
3. C)(2, 3)
4. D)(0, 7)
Show answer
Answer: (2, 3)
Hint: Substitute the x and y values from each option into the equation and check if it satisfies the equality.
Q3.easy
Which of the following points is a solution to the equation 2x + y = 7?
1. A)(1, 4)
2. B)(3, 2)
3. C)(2, 3)
4. D)(4, -1)
Show answer
Answer: (2, 3)
Hint: Substitute the x and y values from each option into the equation and check if it satisfies the equality.
Q4.medium
Which of the following is NOT a solution to the equation 2x + 3y = 12?
1. A)(3, 2)
2. B)(0, 4)
3. C)(6, 0)
4. D)(1, 3)
Show answer
Answer: (1, 3)
Hint: Substitute the x and y values from each ordered pair into the equation. If the left-hand side equals the right-hand side, then it is a solution.
Q5.medium
If the point (k, -2) is a solution of the equation 5x + 2y = 16, what is the value of k?
1. A)4
2. B)2
3. C)-4
4. D)0
Show answer
Answer: 4
Hint: If a point is a solution, its coordinates must satisfy the equation. Substitute the given x and y values into the equation and solve for k.
Q6.medium
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
1. A)x + 2y = 0
2. B)2x = y
3. C)x = 2y
4. D)x - y = 2
Show answer
Answer: x = 2y
Hint: Let 'x' be the cost of the notebook and 'y' be the cost of the pen. Translate the word 'twice' into a mathematical relationship between x and y.
Q7.hard
A linear equation forms a triangle of area 12 square units with the coordinate axes in the second quadrant. If the y-intercept is (0, 6), what is the equation of the line?
1. A)3x + 2y = 12
2. B)3x - 2y + 12 = 0
3. C)2x + 3y = 12
4. D)x - 2y + 6 = 0
Show answer
Answer: 3x - 2y + 12 = 0
Hint: The area of a triangle formed by a line and the axes is (1/2) × |x-intercept| × |y-intercept|. Use this to find the x-intercept.
Q8.hard
For the linear equation ax + by + c = 0, if a + b + c = 0, which of the following points must always be a solution to the equation?
1. A)(1, 1)
2. B)(0, 0)
3. C)(1, 0)
4. D)(0, 1)
Show answer
Answer: (1, 1)
Hint: Try substituting each option's coordinates into the equation and see which one consistently satisfies the given condition.
Q9.hard
The total cost of 'x' pens and 'y' notebooks is ₹300. If the cost of each notebook is ₹20, and the cost of each pen is ₹10, and a customer buys twice as many notebooks as pens, which of the following can be a possible number of pens bought?
1. A)4
2. B)5
3. C)7
4. D)6
Show answer
Answer: 6
Hint: First, form a linear equation based on the total cost. Then, use the relationship between the number of pens and notebooks to eliminate one variable.

These are 9 of the 63 questions available for Linear Equations in Two Variables. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.