# How do you solve the system of equations 4x = 2+ 2y and - \frac { 6} { 5} x + y = \frac { 27} { 5}?

Nov 5, 2017

$x = \frac{37}{8}$ and $y = \frac{33}{4}$

#### Explanation:

$\implies 4 x = 2 + 2 y$

$\implies 4 x - 2 y = 2$ ………[1]

$\implies - \frac{6}{5} x + y = \frac{27}{5}$

Multiply both sides by $2$

$\implies - \frac{12}{5} x + 2 y = \frac{27}{5}$ ………[2]

$4 x - 2 y - \frac{12}{5} x + 2 y = 2 + \frac{27}{5}$

$4 x - \frac{12}{5} x = 2 + \frac{27}{5}$

(4x × 5/5) - 12/5x = (2 × 5/5) + 27/5

$\frac{20 x}{5} - \frac{12 x}{5} = \frac{10}{5} + \frac{27}{5}$

$\frac{20 x - 12 x}{5} = \frac{10 + 27}{5}$

$\frac{8 x}{5} = \frac{37}{5}$

$x = \frac{37}{8}$

Substitute $x = \frac{37}{8}$ in equation [1]

$4 x - 2 y = 2$

(4 × 37/8) - 2y = 2

$\frac{37}{2} - 2 y = 2$

$2 y = \frac{37}{2} - 2$

2y = 37/2 - (2 × 2/2)

$2 y = \frac{37}{2} - \frac{4}{2}$

$2 y = \frac{37 - 4}{2}$

$2 y = \frac{33}{2}$

$y = \frac{33}{4}$