Good morning, Amba. This is going to be way wasier than you think. I promise!
We need to find a value for x and a value for y that makes both equations true. If we were to graph the two equations, the x and y would make the point where the two lines intersect.
There are two ways to solve this without graphing, substitution and elimination. We are going to use substitution.
To use substitution, you need to "solve" one of your equations for x or for y and plug the "value" on the other side of the equal sign for the variable in the other equation.
Since both of your equations are solved for y, we know that the two "values" must be equal, since they both equal y.
(Remember back. If a = b and b = c, then a = c).
Sooooo, we can just set the two values equal to each other...
-4x + 4 = 2x + 2
-6x = -2
x = 1/3
Now that we have a value for x, we plug it into either equation to find y.
y = -4(1/3) + 4
y = -4/3 + 4
y = 2 2/3
So, our solution is (1/3, 2 2/3). If we graphed the two equations, they would intersect at this point.
Let's check...
2 2/3 = -4(1/3) + 4
2 2/3 = -1 1/3 + 4
2 2/3 = 2 2/3. True.
2 2/3 = 2(1/3) + 2
2 2/3 = 2/3 + 2
2 2/3 = 2 2/3. True.
Hope this helps!
