Algebra 9

4 marks · Normal

Solve the following system of equations.

(a)

Given y = x^2 + 1 and x + y = 7, find the two possible values of x.

[3 marks]

(b)

For one of the solutions in part (a), find the corresponding value of y.

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) x = 2 \text{ or } x = -3

(b) y = 5

Common mistakes: Only finding one solution

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Substitutes for y to form x + x^2 + 1 = 7 (or equivalent).

M2 (a) · 1 mark · Forms and solves x^2 + x - 6 = 0, attempts factorisation/quadratic formula.

A1 (a) · 1 mark · Finds both correct values: x = 2 and x = -3.

B1 (b) · 1 mark · Substitutes one value of x into y = x^2 + 1 to find y = 5 (for x = 2) or y = 10 (for x = -3). (follow-through)

Worked solution

a) Substitute y = x^2 + 1 into x + y = 7:

Factorise:

b) For x = 2, y = 2^2 + 1 = 5.