since we want to find solutions that will work for both of the equations, we must first assume that x and y are both the same in both so
y=2x-9
y=-x+6
we make the second equation negative by multiplying the whole thing by -1 and get
-y=x-6
add this to the first equation
y-y=x+2x-9-6
0=3x-15
add 15 to both sides
15=3x
divide both sides by 3
5=x
subsitute 5=x for x in the second equation
y=-x+6
y=-5+6
y=1
