# How do you solve y = 1/5x +4 and x - 5y = -20?

Sep 17, 2015

Have a look:

#### Explanation:

Use the value of $y$ from the first equation substituted into the second and solve for $x$:
$x - 5 \left(\textcolor{red}{\frac{1}{5} x + 4}\right) = - 20$
$x - x - 20 = - 20$
$- 20 = - 20$ true!

The two equations represent COINCIDENT lines. Basically the second is equal to the first multiplied by $5$!
The two lines lie one over the other and so have $\infty$ points in common and the system will then have $\infty$ solutions representing these points.