Well, I just turned in my psychology paper, so I have nothing better to do.
*hears voices telling him to finish his fanfic*
I was going to do that next!
Anyway, here are your equations again.
x - 5y = 2
2x + y = 4
Substitution means you take one of the equations and get one of the variables all by itself on one side. Hopefully, you know how to move terms from one side of the equation to the other. Just think about it this way: when given a true equation (i.e. 1 + 1 = 2), you can add the same thing to both sides of the equation and it would still be true (1 + 1 + 2 = 2 + 2). You can also multiply both sides by the same number, and it would be true. So in any case, let's say you pick the first equation. If you add 5y to both sides, you'll get
x = 2 + 5y
This is also a true equation. Now that we know this, you can write "2 + 5y" every time you see "x" in the other equation. So the second equation will look like this
2(2 + 5y) + y = 4
Using multiplication (you do know how to multiply in parentheses, don't you?), you can get
4 + 10y + y = 4
which leads to
4 + 11y = 4
If you subtract 4 from both sides, you get
11y = 0
Obviously, then, y = 0. Going back to the first equation, you can plug in 0 every time you see "y" and figure out what x is. In this case,
x - 5(0) = 2
which means x = 2.
You can also start out by solving for y. You can solve for y in the first equation, but that gets ugly. Besides, it's not necessary because in the second equation, you can just move the x term to the other side of the equals sign and you'll have a very neat y = 4 - 2x. You can go from there, plugging in "4 - 2x" into the first equation wherever you see "y" and solve it from there in pretty much the same way as I did before. No matter how you start it out, if you do your math correctly, you will always get the same answer for x and y.
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