How do you solve the system of equations -8x + 4y = - 12 and - x - y = - 3?

1 Answer
Jun 8, 2017

x=2
y=1

Explanation:

Equation 1: -8x+4y=-12
Equation 2: -x-y=-3

Because its easier to work with positive values, I'm going to multiple both sides of equation 2 by -1.

x+y=3

I'm going to make y the subject of equation 2 by subtracting x from both sides so I can substitute it into equation 1.

y=3-x

Substitute this value for y into equation 1.

-8x+4(3-x)=-12

Solve for x. Start by expanding the parenthesis.

-8x+12-4x=-12

Then combine the like terms -8x and -4x.

-12x+12=-12

Subtract 12 from both sides of the equation.

-12x=-24

Multiply both sides of the equation by -1 to make them positive.

12x=24

Divide both sides of the equation by 12 to leave x.

x=2

Now we've found x and need to find y. Remember earlier how we found that y=3-x? All we have to do is substitute our value for x into this equation to find y.

y=3-(2)
y=1