CAIE IGCSE Additional Math 5.1 Solve Simultaneous Equations Questions

Practise Cambridge IGCSE Additional Mathematics by solving simultaneous equations and verifying exact solution pairs and intersections.

Exam points

Solve simultaneous equations by substitution, elimination or suitable algebraic transformations.
Handle systems combining linear, quadratic, logarithmic, exponential and rational relationships.
Check all solution pairs in the original equations and report exact coordinates or values.

[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
Correctly eliminates one unknown
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
Factorises or solves their quadratic to get two
solutions
Dep on previous M1

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

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CAIE IGCSE Additional Math 5.1 Solve Simultaneous Equations Questions question 1