Determine how many solutions exist for the system of equations.

Y=2x-9

Y=-x+6

2x-9=-x+6

+x + x

3x-9=6

+9 + 9

3x=15

x=5

therefore the equations have one solution (x=5)

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