The area of shape ABCDEF is $24\text{ cm}^2$. All lengths are in centimetres. The diagram indicates right angles at A, B, C, D, E and F, and the labelled sides are: $AB = 4x$, $BC$ horizontal, $CD$ vertical, $DE = 2x$, $EF = 3x - 9$, and $FA = 3x + 13$. Diagram marked NOT TO SCALE.
(a(i))[3]
Show that $5x^2 + 17x - 12 = 0$.
(a(ii))[3]
Solve, by factorising, the equation $5x^2 + 17x - 12 = 0$. You must show all your working.
(b)[3]
Solve the simultaneous equations $3x - 2y = 23$ and $-4x - y = -5$.