Solutions of ax + by = c: Class 9 practice
A linear equation in two variables has infinitely many solutions. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Solving one-variable equations
The idea behind solutions of ax + by = c
A linear equation in two variables has infinitely many solutions. Pick a value of x, solve for y, and each pair (x, y) is a point on the straight-line graph.
Step-by-step method
- Choose convenient x values (e.g. 0, 1, 2).
- Substitute and solve for y.
- Check each pair in the original equation.
Worked example 1 (Basic)
Check whether (-2, -1) is a solution of 4x + 4y = -12, and find the y-intercept.
- LHS = 4(-2) + 4(-1) = -12 = RHS ✓
- x = 0 → y = -3
- Answer: Yes; y-intercept -3
Worked example 2 (Standard)
Find k if x = 3, y = 2 is a solution of 5x + ky = 17.
- 5(3) + 2k = 17
- 2k = 2, k = 1
- Answer: k = 1
Worked example 3 (Challenge)
Check whether (-2, 6) is a solution of 4x − 4y = -32, and find the y-intercept if it exists.
- LHS = 4(-2) − 4(6) = -32 = RHS ✓
- x = 0 → y = 8
- Answer: Yes; y-intercept 8
Common mistakes and misconceptions
- Thinking there is only one solution
- Substituting into the wrong variable
Practice questions
- (Basic) Check whether (-1, 1) is a solution of 1x + 5y = 4, and find the y-intercept.
- (Basic) Check whether (1, -4) is a solution of 2x + 2y = -6, and find the y-intercept.
- (Standard) Find k if x = 3, y = 2 is a solution of 4x + ky = 6.
- (Standard) Find k if x = 3, y = 2 is a solution of 5x + ky = 15.
- (Challenge) Check whether (4, -2) is a solution of 5x − 4y = 28, and find the y-intercept if it exists.
- (Challenge) Check whether (3, 1) is a solution of 1x − 1y = 2, and find the y-intercept if it exists.
Answer key with full working
- Q1: LHS = 1(-1) + 5(1) = 4 = RHS ✓ → x = 0 → y = 4/5 → Answer: Yes; y-intercept 4/5
- Q2: LHS = 2(1) + 2(-4) = -6 = RHS ✓ → x = 0 → y = -3 → Answer: Yes; y-intercept -3
- Q3: 4(3) + 2k = 6 → 2k = -6, k = -3 → Answer: k = -3
- Q4: 5(3) + 2k = 15 → 2k = 0, k = 0 → Answer: k = 0
- Q5: LHS = 5(4) − 4(-2) = 28 = RHS ✓ → x = 0 → y = -7 → Answer: Yes; y-intercept -7
- Q6: LHS = 1(3) − 1(1) = 2 = RHS ✓ → x = 0 → y = -2 → Answer: Yes; y-intercept -2
Syllabus note
This skill is listed under "Linear Equations in Two Variables" for Class 9 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is solutions of ax + by = c in?
"Linear Equations in Two Variables", Class 9 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.