# How do you solve by substitution  8x - y = 4 and 5x + 3y = 17?

Jun 20, 2015

Answer: $x = 1 , y = 4$

#### Explanation:

$\left\{\begin{matrix}8 x - y = 4 \\ 5 x + 3 y = 17\end{matrix}\right.$

$\left\{\begin{matrix}y = 8 x - 4 \\ 5 x + 3 y = 17\end{matrix}\right.$

Now we can substitute $8 x + 4$ as $y$ in the second equation:

$5 x + 3 \left(8 x - 4\right) = 17$
$5 x + 24 x - 12 = 17$
$29 x = 29$
$x = 1$

Now we substitute $1$ as $y$ in $8 x - y = 4$

$8 \cdot 1 - y = 4$
$y = 4$

So we finally get: $\left\{\begin{matrix}x = 1 \\ y = 4\end{matrix}\right.$