Question

Solve the following system. y = x 2 - 9x + 10 and x + y + 5 = 0. The solutions are

Answer 1

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)

Answer 2

Solution are ( 3,-8) (5 , -10).

Explanation:

Given : y = x² - 9x + 10 and x + y + 5 = 0.

To find : Solve the following system.

Solution : We have given that

y = x² - 9x + 10 -----( equation 1)

x + y + 5 = 0------( equation 2)

First we will solve equation 2 for y

on subtraction both sides by 5

x + y = -5

on subtracting both sides by x

y = -5 -x .

Now plug the value of y in equation 1

-5 -x = x² - 9x + 10

x² - 9x + x +5 + 10 = 0

x² - 8x + 15 = 0

Factoring x² - 5x- 3x + 15 = 0

x ( x -5) -3 (x -5) =0

On grouping (x -3) (x -5)

For x = 3

y = -3 - 5

y = -8.

For x = 5

y = -5 -5

y = -10.

Solution are ( 3,-8) (5 ,- 10)

Therefore, Solution are ( 3,-8) (5 ,-10).