# How do you solve the system by graphing x - 5y = -14 and 3x + y = 6?

Apr 13, 2016

See explanantion

#### Explanation:

Given:
$x - 5 y = - 14$........................(1)
$3 x + y = 6$..........................(2)

$\textcolor{b l u e}{\text{Consider equation (1)}}$

Multiply throughout by (-1)
$- x + 5 y = 14$

Add $x$ to both sides

$- x + x + 5 y = 14 + x$

$0 + 5 y = x + 14$

Divide both sides by 5

$\frac{5}{5} \times y = \frac{x}{5} + \frac{14}{5}$

But $\frac{5}{5} = 1$

$\textcolor{b l u e}{y = \frac{x}{5} + \frac{14}{5}}$.......................(3)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider equation (2)}}$

By the same processes as above we end up with:

$\textcolor{b l u e}{y = - 3 x + 6}$.........................(4)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Plotting equations (3) and (4) we have: