# How do solve the following linear system?:  -x+5y=-5 , -7x+y=-19 ?

May 10, 2016

$x = \frac{45}{17}$ and $y = - \frac{8}{17}$

#### Explanation:

There are several methods to solve simultaneous equations:

Substitution, elimination, or by equating two variables.

Let's make y the subject in both equations:

Equ 1: $5 y = x - 5 \text{ Equ 2} : y = 7 x - 19$
$\text{ } y = \frac{x}{5} - 1$

The two y values are equal: y = y
Therefore: $\frac{x}{5} - 1 = 7 x - 19 \text{ } \times 5$

$x - 5 = 35 x - 95 \text{ solve for } x$
$90 = 34 x$
$\frac{90}{34} = x \Rightarrow \text{ } x = \frac{45}{17}$

Now that we have the value for x, substitute into both equations to check the value for y.

 y = 45/17 ÷ 5 - 1 and $y = 7 \left(\frac{45}{17}\right) - 19$
$y = - \frac{8}{17} \text{ } y = - \frac{8}{17}$