# How do you solve 3x + y = 1 and x – y = 3 using substitution?

May 23, 2018

$\left(x , y\right) = \left(1 , - 2\right)$

#### Explanation:

From the second argument, we can come to conclusion that

$x = 3 + y$

Therefore, we have:

$3 \left(3 + y\right) + y = 1$

Furthermore:

$9 + 3 y + y = 1$

$4 y = - 8$

$y = - 2$

Back to the second equation:

$x = 3 + y$

$x = 3 + \left(- 2\right)$

$x = 1$

So

$\left(x , y\right) = \left(1 , - 2\right)$