Okay, so for this one... you are solving a system of equations. That means you want to find the x,y combination(s), if any, that make both equations true.
There are a couple of different ways to do that, this one is set up to use substitution... since the 2nd equation is y = something... you're going to replace the y in the first equation with that thing (and put it inside parentheses when you replace it!!!)
so 4x = 2y + 6
becomes
4x = 2 (2x -3) + 6
and you clean it up to try to find x... 3 things can happen..
a) you get a # for x, which is half of your ordered pair answer,
b) all the x's go away and what's left over is true like 0=0 or 9=9,
or c) all the x's go away and what's left over is not true like 1 = 9.
As we try to find x in 4x = 2(2x-3)+6 we get
4x = 4x -6 + 6 combine -6 and 6
4x = 4x + 0 subtract 4x from both sides
0 = 0
This is always true, so that means the two equations in your system were actually two descriptions of the same line... so the # of solutions to the system is infinite.
This does NOT mean every single number works, it means there are an unlimited, uncountable # of answers that work... every single x,y combination that makes the first equation true also makes the second equation true.
