Question

Which represents the solution(s) of the system of equations, y = x2 – 4x – 21 and y = –5x – 22? Determine the solution set algebraically.

(–1, –17)
(1, –27)
(–1, –17) and (1, –27)
no solutions

Answer 1

d

Explanation:

on edge 2021

Answer 2

D. No solutions.

Explanation:

We have been given a system of equations and we are asked to find the solution set for our given system.

`y=x^2-4x-21`

`y=-5x-22`

To find the solution for our given system we will equate our both equations as:

`x^2-4x-21=-5x-22`

`x^2-4x+5x-21=-5x+5x-22`

`x^2+x-21=-22`

`x^2+x-21+22=-22+22`

`x^2+x+1=0`

We will use discriminant formula to check for the solution of our given system.

`√(b^2-4ac) \geq 0` for real solutions.

Upon substituting our given values in above formula we will get,

`√(1^2-4*1*1) \geq 0`

`√(1-4) \geq 0`

`√(-3) \\geq 0`

Therefore, our given system has no solutions and option D is the correct choices.