Y=6x-12
Y=-9x+3
Help me solve

First you'll need to solve for x. To do this, put both equations equal to each other
6x-12=-9x+3
Add 9x to both sides
15x-12=3
Add 12 to both sides
15x=15
Divide both sides by 15
x=1
Next, substitute x into one of the equations to find y
y=(6*1)-12
y=6-12
y=-6

So,

Let's solve this algebraically.

Subtract 6x from both sides of the first equation.
y - 6x = -12

Substitute -9x + 3 for y in the first equation.
-9x + 3 - 6x = -12

Collect Like Terms
-15x + 3 = -12

Subtract 3 from both sides
-15x = -15

Divide both sides by -15
x = 1

Substitute 1 for x in the first original equation.
y = 6(1) - 12
y = 6 - 12
y = -6

Check
-6 = 6(1) - 12
-6 = 6 - 12
-6 = -6 This checks.

-6 = -9(1) + 3
-6 = -9 + 3
-6 = -6 This also checks.

S = {(1,-6)}