System of equations

i need to explain the steps in solving a system of equations. I dont know how though.

There are three methods to solving a system of equations:
1) Guess and check:
You just keep guessing values and inserting them until you find one that matches.

2) Combination:
You combine the equations into one big one and solve it.

3) Graphing:
You graph the equations and find where they meet.


Guess and check is a horrible method, but in math, it's always acknowledged as a possible method for finding a solution. Graphing isn't great, but it works. If nothing else, it gives you a ball-park idea of what your solution is. The proper way to do it is combination.

Combination works like this:
y=3x-2
y=-x-6

Well they both = y, and we're trying to find the point where they meet, so we make them equal to each other.
3x-2=-x-6
Let's start by adding x to both sides:
4x-2=-6
Now we add 2 to both sides:
4x=-4
And lastly, we divide both sides by 4:
x=-1

If we plug that into the first equation we get 3(-1)-2=-3-2=-5
If we plug that into the second equation we get -(-1)-6=1-6=-5

Tada, the solution is -5.

As for generalizing the steps for an explanation of how to solve systems of equations in general, you can figure that out for yourself. This is your homework after all, not mine.