iGCSE Mathematics (0580) :E2.5 Derive and solve linear equations in one unknown.iGCSE Style Questions Paper 2

Question

Solve the simultaneous equations.
You must show all your working.

$4x – 2y = -13$
$-3x + 4y = 11$

▶️ Answer/Explanation

Solution

$x = -3$, $y = 0.5$

Multiply first equation by 2: $8x – 4y = -26$

Add to second equation: $5x = -15$ → $x = -3$

Substitute into first equation: $-12 – 2y = -13$ → $-2y = -1$ → $y = 0.5$

Question

Solve the simultaneous equations. You must show all your working.

$2x + y = 3$
$x – 5y = 40$

▶️ Answer/Explanation

Solution

x = 5, y = -7

From first equation: y = 3 – 2x

Substitute into second equation: x – 5(3 – 2x) = 40

Simplify: x – 15 + 10x = 40 → 11x = 55 → x = 5

Substitute x=5 into y=3-2x → y = -7

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