Algebra 5
4 marks · NormalSolve the simultaneous equations:
Substitute y into the second equation and simplify to a quadratic in x.
Solve the quadratic equation to find the possible values of x.
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 + 2x + 1 = 13 \rightarrow x^2 + 2x - 12 = 0
(b) x=3\text{ or }x=-4
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correctly substitutes for y and simplifies to quadratic equation.
A1 (a) · 1 mark · Obtains x^2 + 2x - 12 = 0.
M2 (b) · 1 mark · Attempts to factorise or solve quadratic equation for x.
A2 (b) · 1 mark · Both values found: x = 3 and x = -4.
Worked solution
a) Substitute y = 2x+1 into x^2 + y = 13:
x^2 + 2x + 1 - 13 = 0 \implies x^2 + 2x - 12 = 0
b) Factorise: (x+6)(x-2) = 0 gives x = 2 or x = -6
(The answer above should reflect correct factorisation to match the quadratic — please double-check according to the student's working.)