We start with:
12x + 7y = 3,
4x + 3y = -2.
There are (as far as I know) three methods of solving simultaneous equations. I'll choose substitution. Therefore we must leave either x or y alone. I'll choose x in the second equation (you can choose any of the 2 variables in any of the 2 equations):
4x + 3y = -2,
4x = -3y -2,
x = (-3y - 2)/4.
We now substitute x in the other equation such that:
12x + 7y = 3,
12((-3y - 2)/4) + 7y = 3, 12 and 4 cancel out,
3(-3y - 2) + 7y = 3,
-9y -6 +7y = 3, we now add ys and pass the 6 to the other side,
-2y = 9,
2y = -9,
y = -4.5.
We now substitute y by this value in any of the 2 equations. I'll choose the second one:
4x + 3(-4.5) = -2,
4x - 13.5 = -2, we now pass -13.5 to the other side,
4x = 11.5,
x = 2.875.
Hope it Helps! :D .