CAIE IGCSE Additional Math 5 Simultaneous Equations Topic Practice

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

$$\begin{aligned} (2 x+1)(x+1)=5+2(x+1) \text { or }(2 x-1)(x+1)=5 \text { oe } \end{aligned}$$$2 x^{2}+x-6[=0]$
Factorises or solves their 3-term quadratic
e.g. (x+2)(2 x-3)
$\left(\frac{3}{2}, 4\right)$

Correct elimination of one unknown e.g.
$$\begin{aligned} \left(\frac{3}{2}\right)^{4} \times \frac{1}{x}=\frac{27}{16} \text { or }\left(\frac{3}{2} x\right)^{4} \times \frac{1}{x^{5}}=\frac{27}{16} \text { or } \frac{y^{4}}{\left(\frac{2 y}{3}\right)^{5}}=\frac{27}{16} \text { or } 16\left(\frac{81}{16} x^{4}\right)=27 x^{5} \text { or } 16 y^{4}=27\left(\frac{32}{243} y^{5}\right) \mathrm{oe} \end{aligned}$$
x=3 and $y=\frac{9}{2}$ oe and no other solutions
A1 for x=3 or $y=\frac{9}{2}$ oe