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

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

Step-by-step 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).

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