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

1 Answer
Mark S.
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

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