How do you solve by substitution -x + 2y = -6 and 3x + y = 8?

Apr 29, 2018

$\left(\frac{22}{7} , - \frac{10}{7}\right)$

Explanation:

In the second equation, we can easily solve for $y$ by subtracting $3 x$ from both sides. We get:

$y = 8 - 3 x$

We've already solved for one variable in terms of the other, so we can plug into the first equation. We get

$- x + 2 \left(8 - 3 x\right) = - 6$

$\implies - x + 16 - 6 x = - 6$

$\implies - 7 x + 16 = - 6$

We can subtract $16$ from both sides to get

$- 7 x = - 22$

Dividing both sides by $- 7$, we get

$\textcolor{b l u e}{x = \frac{22}{7}}$

We can plug into our equation for $y$, $y = 8 - 3 x$. We get

$y = 8 - 3 \left(\frac{22}{7}\right)$

$y = \frac{56}{7} - \frac{66}{7}$

$\textcolor{\lim e}{y = - \frac{10}{7}}$

Hope this helps!