What is the solution set of this system of equations? y=x2-7 y=-x+5 The solution set of a system of equations is the set of all values that satisfy all the equations

The answer to your question is (-4, 9) and (3, 2)

Step-by-step explanation:

Data

Equation 1 y = x² - 7

Equation 2 y = - x + 5

Process

1. - Substitute Equation 2 in equation 1

-x + 5 = x² - 7

2. - Equal to zero

x² + x - 7 - 5 = 0

x² + x - 12 = 0

3. - Factor to find x

(x + 4) (x - 3) = 0

x₁ + 4 = 0 x₂ - 3 = 0

x₁ = - 4 x₂ = 3

4. - Substitute x₁ and x₂ to find y

y = - x + 5 x₁ = - 4

y = - (-4) + 5

y = 4 + 5

y = 9 Solution (-4, 9)

y = - x + 5 x₂ = 3

y = - 3 + 5

y = 2 Solution (3, 2)