GCSE · Simultaneous equations

Simultaneous equations — one linear, one quadraticExam-style questions

Why a line can meet a curve twice (so expect two solution PAIRS), why substitution is the only route in, and the bracket-squaring discipline that circle equations demand.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 4 Level 5

1
Solve the simultaneous equations

$x^2 + y^2 = 25$ $y = x + 1$

Give your answers as coordinate pairs.
Level 5 · 5 marksTry it
2
The line $y = x - 3$ meets the circle $x^2 + y^2 = 17$ at the points $A$ and $B$ .

(a) Show that $2x^2 - 6x - 8 = 0$ at the points $A$ and $B$ .

(b) Find the coordinates of $A$ and $B$ .
Level 5 · 5 marksTry it
3
Show that the line $y = 2x - 5$ meets the curve $y = x^2 - 4x + 4$ at exactly one point, and find the coordinates of that point.
Level 5 · 3 marksTry it
4
Solve the simultaneous equations

$x^2 + y^2 = 52$ $y = x - 2$

Give your answers as coordinate pairs.
Level 5 · 4 marksTry it
5
Solve the simultaneous equations

$x + y = 7$ $y = x^2 - 5x + 10$
Level 5 · 4 marksTry it

2 more questions on simultaneous equations — one linear, one quadratic

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