# Simultaneous Equations Long Questions (Question 1 & 2)

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

Question 2:
Solve the following simultaneous equations.
x – 3y + 5 = 3y + 5y2– 6 – x = 0

Solution:
x – 3y + 5 = 0
x = 3y – 5 —–(1)
3y + 5y2 – 6 – x = 0 —–(2)

Substitute (1) into (2),
3y + 5y2 – 6 – (3y – 5) = 0
3y + 5y2 – 6 – 3y + 5 = 0
5y2 – 1 = 0
5y2  = 1
y±0.447

Substitute the values of y into (1),
When y = 0.447
x = 3 (0.447) – 5
x = –3.659

When y = – 0.447
x = 3 (–0.447) – 5
x = –6.341

The solutions are x = –3.659, y = 0.447 and x = –6.341, y = – 0.447.