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

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