Question

Solve the following system. y = x 2 - 9x + 10 and x + y + 5 = 0. Enter the solution with the smaller x value first.

Answer 1

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

Answer 2

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)