Question

How do you solve the system of equations `2x-2y=-8` and `x+2y=-1`?

Answer 1

Add the 2 equations together to arrive at `x=(-3)` and `y=1`

Explanation:

When solving a system of equations we need to reduce the system down to a more simple form. Here, we have two equations and two unknowns, so we have everything we need to solve it.

Remember that the values of x and y in equation 1 are the same as in equation 2 (so if you were to graph these two lines, the solution is where they intersect). Because the x's are the same in equations 1 and 2, as are the y's, we can add and subtract them against each other.

What we really want at this point is not 2 equations with 2 unknowns, but 1 equation with one unknown. Looking at the 2 equations, I see a -2y term in first and a +2y in the second, so if we add the 2 equations together, the y terms will fall away, like this:

`2x-2y = -8`
+`(x+2y=-1)`

We add the separate terms together (so the 2x + x = 3x, -2y +2y = 0, and -8 + (-1) = -9) and get

`3x = -9`

divide both sides by 3 and we get

`x=-3`

To find y, we can substitute -3 for x in either equation (the first or second) and get y. I always like to do both as a check figure - if I get 2 different answers, I know I've made an error somewhere.

`2*(-3) - 2y = -8`
`-6-2y = -8`
`-2y=-2`
`y=1`

`-3+2y=-1`
`2y=2`
`y=1`