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, –2…

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asked Apr 25, 2017 206k views

2 Answers

Wilywampa · Answer 1 · 2017-04-30T03:29:15+0000

Answer:

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.