Answer:
x = -2 and y = -8
Explanation:
STEP 1: the first step in solving the system of equations, we need to isolate one variable for one equation and then plug in the resulting equation into the other equation
13x - 6y = 22
x = y + 6
looking at our 2 equations, we see that x is by itself in the 2nd equation, so this has made it easy for us! we can now substitute y + 6 into 13x - 6y = 22 where y + 6 = x
13(y + 6) - 6y = 22 < distribute 13 into y + 6
13y + 78 - 6y = 22 < combine like terms
7y + 78 = 22 < we want to get y alone, so subtract 78 from both sides
-78 -78
7y = -56 < to get y alone, divide both sides by 7
7y/7 = y
-56/7 = -8
y = -8
STEP 2: we have now found our y, so the next step is to plug in the value we have for y into one of the original equations and solve for x. i have chosen x = y + 6, but you can do it for 13x - 6y = 22 as well
x = (-8) + 6 < add
x = -2
so our x value is -2, if you were to plug in y = -8 into 13x - 6y =22 you would get the following:
13x - 6(-8) = 22
13x + 48 = 22 < subtract 48 from both sides
-48 -48
13x = -26 < divide both sides by 13
13x/13 = x
-26/13 = -2
x = -2
our final answer is x = -2 and y = -8