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

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

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)