I further broke this down to:

2x + 3y = -9

and

2x + 3y = 18

In order for me to apply the addition method to this, I need to make the coefficient of one of the variables equal and opposite. I assume that means I multiply the first equation by 2 and the second by -2.

So I would get 2*2x+2*3y=2*-9, which equals 4x+6y=-18 for equation 1.

For equation two I would get -2*2x+-2*3y=-2*18, which equals -4x-6y=-36.

Using the addition method and adding equation one and two together, this all looks good for 'x', but my 'y' value also becomes zero, which leaves me no equation for the -54. I essentially get 0x + 0y = -54, which doesn't work.

Where am I going wrong here, please?