AmbifulWorksheets
Practice that never repeats
CBSE · Class 9 · Mathematics

Two Variables, One Line

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
Which point lies on the line x − y = 0?
  1. (2, 1)
  2. (3, 2)
  3. (1, 2)
  4. (2, 2)
2.
If (7, k) is a solution of 9x + 8y = 127, then k equals:
  1. 127
  2. 9
  3. 8
  4. −8
3.
The equation y = −6x + 9 in the form ax + by + c = 0 is:
  1. −6x − y − 9 = 0
  2. x + 6y + 9 = 0
  3. −6x + y + 9 = 0
  4. −6x − y + 9 = 0
4.
The line 8x + 6y = −24 meets the x-axis at:
  1. (−3, 0)
  2. (−3, −3)
  3. (0, −3)
  4. (−24, 0)
5.
A linear equation in two variables has:
  1. no solution
  2. infinitely many solutions
  3. exactly one solution
  4. exactly two solutions
6.
The line 6x + 3y = 24 meets the y-axis at:
  1. (0, 8)
  2. (0, −8)
  3. (8, 0)
  4. (0, 24)
7.
Which equation has (−1, −5) as a solution?
  1. 3x + 9y = −48
  2. 3x − 9y = −48
  3. 3x + 9y = −47
  4. 3x + 9y = −51
8.
Assertion (A): (1, 3) is a solution of 4x − 6y = −20.
Reason (R): A pair (x, y) is a solution if it makes both sides of the equation equal.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Find two solutions of 2x + 7y = 70.
10.
Is (3, −1) a solution of 8x + 3y = 23? Give a reason.
11.
Find k if (2, 2) lies on the line kx + y = 14.
12.
Express x in terms of y: 5x − 5y = −17
13.
For the equation 9x + 2y = 81, find y when x = 7.
14.
The cost of a bat is 9 times the cost of a ball. Write a linear equation (x = cost of a bat, y = cost of a ball).
15.
Find the point on the line 4x − 6y = −12 whose x- and y-coordinates are equal.
16.
Find where the line 8x + 9y = 216 meets the x-axis and the y-axis.
Section C — Word problems4 × 4 = 16 marks
17.
A taxi charges Rs 46 for the first km and Rs 16 for every km after that. Write an equation for the fare y for x km, and find the fare for 12 km.
18.
Ananya's age is 8 years more than 4 times Isha's age. Write a linear equation (x = Ananya's age, y = Isha's age), and find Ananya's age when Isha is 11.
19.
Temperature in Fahrenheit is F = (9/5)C + 32. Find F when C = 25, and find C when F = 14.
20.
A mobile plan costs Rs 190 a month plus Rs 50 for each GB of data. Write an equation for the bill y when x GB are used. How many GB were used if the bill is Rs 290?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 9 · Mathematics

Answer key

Two Variables, One Line · AW-9M-LE2-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) (2, 2)1 × 2 + (−1) × 2 = 0
2(c) 89 × 7 + 8k = 127, so k = 8
3(d) −6x − y + 9 = 0move y to the right-hand side
4(a) (−3, 0)put y = 0: 8x = −24, x = −3
5(b) infinitely many solutions—
6(a) (0, 8)put x = 0: 3y = 24, y = 8
7(a) 3x + 9y = −483 × (−1) + 9 × (−5) = −48
8(d) A is false, but R is true.A is false: 4 × 1 + (−6) × 3 = −14, not −20. R is true.
9e.g. (0, 10) and (35, 0)x = 0 gives y = 10; y = 0 gives x = 35
10No8 × 3 + 3 × (−1) = 21, not 23
11k = 62 × k + 1 × 2 = 14, so k = 6
12x = (−17 + 5y)/55x = −17 + 5y
13y = 99 × 7 + 2y = 81, so 2y = 18
14x − 9y = 0x = 9y
15(6, 6)put x = y: −2x = −12, so x = y = 6
16(27, 0) and (0, 24)y = 0 gives x = 27; x = 0 gives y = 24
17y = 16x + 30; Rs 222y = 46 + 16(x − 1) = 16x + 30; y = 16 × 12 + 30 = 222
18x − 4y − 8 = 0; 52 yearsx = 4y + 8 = 4 × 11 + 8 = 52
19F = 77; C = −10(9/5) × 25 + 32 = 77; (14 − 32) × 5/9 = −10
20y = 50x + 190; 2 GB50x + 190 = 290; 50x = 100; x = 2