0580/32 Feb/Mar 2024, Question 7: Solving Linear Equations

Part (a) · 1 mark

Substitute a = 2 into P = 3a + 5 and calculate P.

1. 1P = 3 × 2 + 5
2. 2P = 11

Answer11

Part (bi) · 1 mark

Solve the equation 7x = −42 for x.

1. 1x = −42 ÷ 7
2. 2x = −6

Answer−6

Part (bii) · 3 marks

Solve 9(8x − 7) = 72 for x.

1. 18x − 7 = 72 ÷ 9 = 8
2. 28x = 15
3. 3x = 15/8 = 1.875

Answer1.875

Part (c) · 1 mark

Given 5⁸ × 5ᵏ = 5⁻²⁴, find the value of k.

1. 18 + k = −24
2. 2k = −32

Answer−32

Part (d) · 2 marks

Solve the simultaneous equations −6x − y = 13 and 8x + y = −51.

1. 1Add the equations: 2x = −38
2. 2x = −19
3. 38(−19) + y = −51, so y = −51 + 152
4. 4y = 101

Answerx = −19, y = 101

Part (e) · 2 marks

List all integer values of n satisfying n > −3 and n ≤ 1.

1. 1n > −3 excludes −3; n ≤ 1 includes 1
2. 2n = −2, −1, 0, 1

Answer−2, −1, 0, 1

Part (f) · 2 marks

Write an expression in x and t for total metres walked 35 minutes at x m/min then run t minutes at 160 m/min.

1. 1Walking distance = 35 × x = 35x
2. 2Running distance = 160 × t = 160t
3. 3Total = 35x + 160t

Answer35x + 160t

Part (g) · 3 marks

Find the area of a rectangle with sides x − 2 and x + 5, giving it as x² + ax + b.

1. 1Area = (x + 5)(x − 2)
2. 2= x² − 2x + 5x − 10
3. 3= x² + 3x − 10

Answerx² + 3x − 10

More past-paper questions on solving linear equations

• 0580/12 May/Jun 2026 Q10 · 4 marks
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