# X-12y=-7 3x-6y=-21 how do I solve ?

May 2, 2018

Use linear combination to eliminate one term in the equation.

#### Explanation:

The goal is to completely remove one variable from both sets of equations. The best way to do this is to combine both equations and manipulate them beforehand for elimination.

$x - 12 y = - 7$
$\left(3 x - 6 y = - 21\right) \times 2$

Multiply this equation by $2$ so you have $12 y$ in both. Then, add/ subtract the equations from each other (choose the operation that will eliminate a variable, so in this case it is subtraction)

$x - 12 y = - 7$
$6 x - 12 y = - 42 \text{ " " }$ Subtract them straight down.

$- 5 x = 35$

$x = \frac{- 35}{5}$

$x = - 7$

Plug $x$ into either equation to solve for $y$.

$- 7 - 12 y = - 7$

$- 12 y = 0$

$y = 0$