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

1 Answer
Mark S.
Jun 8, 2017

x=2x=2
y=1y=1

Explanation:

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

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

y=3-xy=3−x

Substitute this value for yy into equation 1.

-8x+4(3-x)=-12−8x+4(3−x)=−12

Solve for xx. Start by expanding the parenthesis.

-8x+12-4x=-12−8x+12−4x=−12

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

-12x+12=-12−12x+12=−12

Subtract 12 from both sides of the equation.

-12x=-24−12x=−24

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

12x=2412x=24

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

x=2x=2

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

y=3-(2)y=3−(2)
y=1y=1

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