X+y+5=0 y=-x-5 If a solution exists y=y so we can say x^2-9x+10=-x-5 add x+5 to both sides x^2-8x+15=0 now factor x^2-3x-5x+15=0 x(x-3)-5(x-3) (x-5)(x-3) so x=3 and 5, using y=-x-5 y(3)=-8 and y(5)=-10 So the two solutions are: (3,-8) and (5,-10)
To solve the system, we need to set the two equations equal to each other. However, we need to manipulate the equations so they equal the same thing. y=x^2-9x+10
x+y+5=0 y= -5-x
Now that we have two equations that both equal y, we can set them equal to each other and solve for x. -5-x=x^2-9x+10 0=x^2-8x+15 0=(x-5)(x-3) 0=x-5 0=x-3 x=5 x=3
