#### Answer

x = -6
y = 2

#### Work Step by Step

-x + 2y = 10
-2x + 3y = 18
minus 2y to both sides to the first equation
-x + 2y - 2y = 10 - 2y
-x = 10 - 2y multiply by -1 both sides
-1 ( -x ) = -1 ( 10 - 2y ) use the distributive property
x = -10 + 2y distributive x to the second equation
-2 ( -10 + 2y ) + 3y = 18 use the distributive property
20 - 4y + 3y = 18
20 -y = 18 minus 20 to both sides
20 - y - 20 = 18 - 20
-y = -2 multiply by -1
y = 2 substitude y to x = -10 + 2y
x = -10 + $2\times2$
x = -10 + 4
x = -6