# What are x and y if -3x+y=6 and 6x-2y=25??

Oct 24, 2015

It is impossible for both
$\textcolor{w h i t e}{\text{XXX}} - 3 x + y = 6$
and
$\textcolor{w h i t e}{\text{XXX}} 6 x - 2 y = 25$
for any pair of values $\left(x , y\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} - 3 x + y = 6$
and
[2]$\textcolor{w h i t e}{\text{XXX}} 6 x - 2 y = 25$

If we multiply [1] by $\left(- 2\right)$, we get
[3]$\textcolor{w h i t e}{\text{XXX}} 6 x - 2 y = - 12$

Comparing [2] and [3], we have
$\textcolor{w h i t e}{\text{XXX}} 25 = - 12$ (Impossible)

The given equations represent two parallel lines (they have no points in common).