# How do you solve the system of equations 3x - y = - 10 and x - y = 2 by elimination?

How do you solve the system of equations 3x - y = - 10 and x - y = 2 by elimination?

ReportAnswer 1

The solution set is $\left(- 6 , - 8\right)$.

#### Explanation:

We've got $3 x - y = - 10$, and $x - y = 2$

So now, we can take $x - y = 2$ as $y - x = - 2$.

Now simply add the two equations:

$\left(3 x - y\right) + \left(y - x\right) = - 10 + \left(- 2\right)$

$2 x = - 12$

$x = - 6$

So if $x = - 6$, $y$ can be found by substitution:

$3 \left(- 6\right) - y = - 10$

$- 18 - y = - 10$

$- y = 8$

$y = - 8$

So here, $x = - 6 , y = - 8$, and the solution set is $\left(- 6 , - 8\right)$.

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