# How do you solve the system of equations 3x+7y=57 and -6x+2y=-18?

Mar 27, 2017

Complex linear systems can be solved in matrix form using Cramer's Rule. Simple ones like this one can be arranged according to their factors and solved algebraically.

#### Explanation:

Arrange the equations so that the factors align, with all of the similar variables on one side:
3x + 7y = 57
−6x + 2y = −18
Then algebraically combine them. You can use multiplicative factors to an entire equation if the coefficients are not already equal. In this case multiplying the first equation by ‘2’ will allow us to eliminate the 'x' coefficients. Simply add the second equation to the first to get a single equation in only the 'y' variable.

2*(3x + 7y = 57)
−6x + 2y = −18

$6 x + 14 y = 114$
-6x + 2y = −18
$16 y = 96$

y = 6

Substitute this value back into one equation to solve for 'x', then use the other equation to check the final values for correctness.
3x + 7(6) = 57 ; 3 x = 57 – 42 ; 3x = 15 ; x = 5
CHECK:
−6(5) + 2(6) = −18 ; -30 + 12 = - 18 ; -18 -= -18 CORRECT!
Solution Set: y = 6, x = 5