6.4.7 Linear Equations, PT3 Focus Practice

Question 19:
Calculate the value of x and of that satisfy the following simultaneous linear equations:
$\begin{array}{l}x+6y=12\\ \frac{2}{3}x+2y=6\end{array}$
[4 marks]
Solution:
$\begin{array}{l}x+6y=12\\ x=12-6y---\left(1\right)\\ \frac{2}{3}x+2y=6\\ \left(×3\right)2x+6y=18\\ \left(÷2\right)x+3y=9---\left(2\right)\end{array}$

Substitute (1) into (2),
12 – 6y + 3= 9
–3y = –3
= 1
Substitute y = 1 into (1),
x = 12 – 6 (1)
x = 6