Question

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

Answer 1

Answer:

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)