Determine how many solutions exist for the system of equations.
Y=2x-9
Y=-x+6

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 soy=2x-9y=-x+6we make the second equation negative by multiplying the whole thing by -1 and get-y=x-6add this to the first equationy-y=x+2x-9-60=3x-15add 15 to both sides15=3xdivide both sides by 35=xsubsitute 5=x for x in the second equationy=-x+6y=-5+6y=1

2x-9=-x+6+x      +x3x-9=6    +9 +93x=15x=5therefore the equations have one solution (x=5)