Algebra 9

3 marks · Normal

Solve the following simultaneous equations for x and y:

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x = 2 \text{ or } x = -3; y = 4 \text{ or } y = 9

Also accept: x = -3, y = 9 and x=2, y=4

Common mistakes: Only one solution pair found

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Marking points

M1 · 1 mark · Substitute y = x^2 into x + y = 7, forming quadratic.

M2 · 1 mark · Solve x^2 + x - 7 = 0 for both x values.

A1 · 1 mark · Both correct solution pairs: (x=2, y=4) and (x=-3, y=9).

Worked solution

Substitute y from the second equation into the first:

Solve the quadratic: (x + 3)(x - 2) = 0, so x = -3 or x = 2.

For x = -3: y = (-3)^2 = 9.

For x = 2: y = 2^2 = 4.