# 4.2.4 Simultaneous Equations, Long Questions (Question 7 & 8)

4.2.4 Simultaneous Equations, Long Questions
Question 7:
Solve the following simultaneous equations.
5y – 6x= 2
$\frac{4y}{x}-\frac{3x}{y}=4.$

Solution:
5y – 6x= 2 —– (1)

Substitute (3) into (2),
$\begin{array}{l}\frac{4\left(\frac{2+6x}{5}\right)}{x}-\frac{3x}{\left(\frac{2+6x}{5}\right)}=4\\ \frac{8+24x}{5x}-\frac{15x}{2+6x}=4\\ \frac{\left(8+24x\right)\left(2+6x\right)-\left(15x\right)\left(5x\right)}{5x\left(2+6x\right)}=4\end{array}$

16 + 48x + 48x + 144x2 – 75x2 = 20x (2 + 6x)
69x2 + 96x + 16 = 40x + 120x2
51x2 – 56x – 16 = 0
(3x – 4)(17x + 4) = 0
3x – 4 = 0 or 17x + 4 = 0

Question 8:
Solve the following simultaneous equations.
$\begin{array}{l}x+2y=1\\ 2{x}^{2}+{y}^{2}+xy=5\end{array}$