# How do you solve -20x+7y=137, 4x+5y=43?

May 19, 2018

$x = - 3$
$y = 11$

#### Explanation:

you have 2 equations and 2 unknowns so let's solve by elimination:

$- 20 x + 7 y = 137$
$\text{ } 4 x + 5 y = 43$

$- 20 x \mathmr{and} 4 x \text{ have a common denominator } 20 x$ so multiply the bottom equation by 5:

$- 20 x + 7 y = 137$
$5 \left(4 x + 5 y = 43\right)$

$- 20 x + 7 y = 137$
$\text{ } 20 x + 25 y = 215$

now add the equations together, notice the x terms cancel:

$32 y = 352$

$y = 11$

finally insert y's value in to either of the original equations to solve for x:

$4 x + 5 y = 43$

$4 x + 5 \left(11\right) = 43$

$4 x + 55 = 43$

$4 x = - 12$

$x = - 3$