Linear Equations in Two Variables is where your child meets equations like 2x + 3y = 6 — statements with a whole line of solutions rather than a single answer. The chapter builds the habit of substituting a value, checking whether a point lies on a line, writing an equation in standard form ax + by + c = 0, and turning a word problem into a pair of equations. These are gentle, high-scoring skills once practised, and they lead straight into the Class 10 work on simultaneous equations.

This free printable worksheet has 12 questions from Bmathpro’s own question bank of 10,500+ validated maths questions — the same bank our enrolled students practise from. Every answer comes with a one-line explanation, so you can check your child’s method, not just the final answer.

Set aside 15–20 minutes, keep the answers hidden until the end, and let your child attempt every question — a wrong attempt tells you more than a skipped one.

What this worksheet covers

• Recognising a linear equation in two variables
• Finding a value that makes a point a solution
• Checking whether a given point lies on a line
• Writing an equation in standard form ax + by + c = 0
• Using a solution common to two equations
• Word problems that form linear equations

Maps to the CBSE Class 9 Linear Equations in Two Variables chapter (NCERT) and equivalent ICSE/State-board units.

Class 9 Linear Equations in Two Variables Worksheet — 12 Questions

Warm-up

1. If x = 2 and y = 3 is a solution of the equation x + y = k, find the value of k. (Write your answer.)

2. A line is y = 4x + 3. Find y when x = 6. (Write your answer.)

3. How many solutions does a linear equation in two variables have?
A. Exactly one  B. Infinitely many  C. No solution  D. Exactly two

4. Which of the following is a linear equation in two variables?
A. x² + y = 4  B. xy = 5  C. 2x + 3y = 6  D. x + 1 = 0

Building up

5. The point (3, k) lies on 2x + 5y = 31. Find k. (Write your answer.)

6. In x + 5y = 25, find y when x = 5. (Write your answer.)

7. In 2x + 3y − 6 = 0, what is the value of c (comparing with ax + by + c = 0)? (Write your answer.)

8. Does (2, 2) satisfy 2x + 3y = 10?
A. No  B. Yes

Challenge

9. In 4x + 3y = 15, find y when x = 3. (Write your answer.)

10. Write x = 4y in the standard form ax + by + c = 0. (Write your answer.)

11. If x = 2, y = 1 is a solution of both ax + 3y = 11 and 2x + by = 7, find a + b. (Write your answer.)

12. A juice stall sells two cup sizes. Each small cup costs ₹15 and each large cup costs ₹25. One afternoon the stall sold a total of 12 cups and collected exactly ₹240. How many large cups were sold? (Write your answer.)

🖨️ Print this worksheet

Answer key with explanations

Show answers and explanations (parents — open this after your child finishes)

1. 5 — k = 2 + 3 = 5.
2. 27 — y = 24 + 3 = 27.
3. B. Infinitely many — every point on the line is a solution.
4. C. 2x + 3y = 6 — both variables to the first power.
5. 5 — 6 + 5k = 31 → k = 5.
6. 4 — 5 + 5y = 25 → y = 4.
7. −6 — comparing with ax + by + c = 0, c = −6.
8. B. Yes — 4 + 6 = 10.
9. 1 — 12 + 3y = 15 → y = 1.
10. x − 4y = 0 — a = 1, b = −4, c = 0.
11. 7 — a = 4 and b = 3, so a + b = 7.
12. 6 — x + y = 12 and 15x + 25y = 240 give y = 6 large cups.

How to use this worksheet at home

• Keep it short and calm. 15–20 minutes beats an hour of pressure.
• Substitute carefully. Most slips here come from plugging a value into the wrong variable — ask your child to write x = … and y = … clearly before substituting.
• Praise the method, not the marks. (We deliberately don’t put marks on our worksheets.)

FAQs

Is this worksheet free to print?
Yes — free to use and print at home, no sign-up needed.

Which syllabus does it follow?
Standard Class 9 Linear Equations in Two Variables chapter — CBSE (NCERT), ICSE and State boards.

Why does one linear equation in two variables have infinitely many solutions?
Because it represents a whole straight line — every point (x, y) on that line satisfies it. You need a second equation to pin down a single point, which is the Class 10 work. A free demo class shows how this connects.

Where can my child get more practice like this?
Enrolled students get Math Gym, our paid practice app with 10,500+ questions — see our courses page.

Also practise: Polynomials · Number Systems · Linear Equations in Two Variables · all Class 9 worksheets.

Did your child enjoy these questions?

See how they do with a real teacher beside them. Book a free demo class — your child meets a Bmathpro teacher and you see how our small-batch online maths classes for Class 9 work. No fee, no obligation.

Questions? WhatsApp us: +91 89198 52512