1. Ok, so we know that this has no solution. To prove that, we're going to first get one variable on a single side of the equation. For that, we'll do the first equations' x.
3x - 6y = -12 : Add 6y to both sides
3x = 6y - 12 : Divide by 3
x = 2y - 4
Ok, so what we get from that is that x IS 2y-4, so we'll plug that in for the other equation.
2y - 4 - 2y = -8 : Combine like terms
0y - 4 = -8 : Add 4
0y = -4
0 = -4
Ok, so there's no solution to that one. There aren't any variables left, therefore it is unsolvable.
The two lines in this system of equations will never intersect.
2.
2x - 3y = 13
x + 2y = -4 : Let's multiply this equation by negative two, so that the x's will cancel out.
2x - 3y = 13
-2x - 4y = 8 : Now we combine these two equations.
-7y = 21 : Divide by -7
y = -3 : Now we'll plug this -3 in for y in whatever equation. I'll choose the second one.
x + 2(-3) = -4
x + -6 = -4
x = 2
So our y is -3, and our x is 2, so our solution is (2, -3).
3 is beyond my knowledge, but I was happy to help you on 1 and 2.
