How many solutions does the following system have?
-3x-2y=-12
9x+6y=-6
I know that they have no solutions but I just don't understand why.. Help?

Question

How many solutions does the following system have?
-3x-2y=-12
9x+6y=-6
I know that they have no solutions but I just don't understand why.. Help?

mhchen · Answer

You can make the 2 equations the same on one side.
If you multiply the top equation by -3, It becomes:
-3(-3x-2y) = (-12)-3
9x + 6y = 36
^^^^^^
You see how we got 9x + 6y = something?
In the other equation, we ALSO got 9x + 6y = something.

So that means the 'something' has to be the same, but -6 does NOT equal to 36.

Therefore this system of equations is impossible to solve.