CAIE IGCSE Additional Math 5.1 solve simultaneous equations

Use this simultaneous-equations page to substitute one equation into another, reduce to a solvable equation and pair the solutions.

Exam points

Use substitution to reduce simultaneous equations involving products or squares.
Solve the resulting quadratic or exact equation before pairing x and y values.
Give answers in requested exact forms such as a+b√3 when required by the question.

[Maximum number: 5]

Solve the simultaneous equations

\begin{array}{r} \lg (x+2 y)=0 \\ x^{2}+4 x y+y=1 \end{array}

x+2 y=1

B1

Correctly eliminates one unknown

M1

Dep on B1 allow unsimplified e.g.
$x=1-2 y \text { or } y=\frac{1-x^{2}}{4 x+1}$

Correct quadratic in solvable form:
$y-4 y^{2}[=0]$ oe or
$2 x^{2}-3 x+1[=0]$ oe

A1

Factorises or solves their quadratic to get two
solutions

M1

Dep on previous M1

y=0, x=1 and $y=\frac{1}{4}, x=\frac{1}{2}$

A1

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5.1. Solve simultaneous equations question 1