What are x and y if 4x−4y=−16 and x−2y=−12?

1 Answer
Lotusbluete
Nov 10, 2015

x=4, y=8

Explanation:

There are many ways to solve a system of linear equations.
One of those goes like this:

Take the equation that looks easier to you and solve it for x or y, whichever is easier.
In this case, if I were you, I would definitely take x−2y=−12 and solve it for x:

x−2y=−12
⇔x=2y−12

Now, plug 2y−12 for x in the other equation:

4⋅(2y−12)−4y=−16

...simplify the left side:
⇔8y−48−4y=−16
⇔4y−48=−16

... add 48 on both sides:
⇔4y=48−16
⇔4y=32

... divide by 4 on both sides:
⇔y=8

Now that you have the solution for y, you just need to plug this value into one of the two equations (again, whichever is easier) and compute x:

x−2⋅8=−12
⇔x=16−12
⇔x=4

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