What are x and y if 4x-4y=-164x−4y=−16 and x-2y=-12x−2y=−12?

1 Answer
Lotusbluete
Nov 10, 2015

x = 4x=4, y = 8y=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 xx or yy, whichever is easier.
In this case, if I were you, I would definitely take x - 2y = -12x−2y=−12 and solve it for xx:

x - 2y = - 12x−2y=−12
<=> x = 2y - 12⇔x=2y−12

Now, plug 2y - 122y−12 for xx in the other equation:

4*(2y-12) - 4y = -164⋅(2y−12)−4y=−16

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

... add 4848 on both sides:
<=> 4y = 48 - 16⇔4y=48−16
<=> 4y = 32⇔4y=32

... divide by 4 on both sides:
<=> y = 8⇔y=8

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

x - 2* 8 = - 12x−2⋅8=−12
<=> x = 16 - 12⇔x=16−12
<=> x = 4⇔x=4

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