# How do you solve the linear system by substitution 3x + y =2 and -x -3y=6?

Apr 28, 2018

Like so:

#### Explanation:

$3 x + y = 2$

$- x - 3 y = 6 \implies - 6 - 3 y = x$

Substitute this equation into the other system wherever you see $x$.

$3 \left(- 6 - 3 y\right) + y = 6$

Distribute $3$ onto $\left(- 6 - 3 y\right)$

$- 18 - 9 y + y = 2$

Combine alike terms

$- 8 y = 20$

Divide to solve for $y$

$\frac{- 8 y}{-} 8 = \frac{20}{- 8} \implies y = - \frac{20}{8}$

Then solve for $x$ using the value of $y$.

$- x - \frac{60}{8} = 6$

$x = - \frac{108}{8}$

$y = - \frac{20}{8}$

Hope that helps!