# How do you solve this system of equations: 6x + 5y = 300 and 3x + 7y = 285?

May 20, 2018

$x = 25$
$y = 30$

#### Explanation:

$6 x + 5 y = 300$
$3 x + 7 y = 285$

Using elimination we need to find a common denominator of the coefficient of either x or y; this one looks like x is easier:

LCD of 6 and 3 is 6 so let's multiply the second equation by $- 2$:

$- 2 \left(3 x + 7 y = 285\right)$

$- 6 x - 14 y = - 570$

$\text{ } 6 x + 5 y = 300$
$- 6 x - 14 y = - 570$

$- 9 y = - 270$

$y = 30$

insert y into either of the original equations to solve for x:

$3 x + 7 y = 285$

$3 x + 7 \left(30\right) = 285$

$x = 25$