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

Answer:

D. No solutions.

Step-by-step 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.

$\sqrt{b^2-4ac} \geq 0$ for real solutions.

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

$\sqrt{1^2-4*1*1} \geq 0$

$\sqrt{1-4} \geq 0$

$\sqrt{-3} \ngeq 0$

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

Answer 2

Hello,

With
y=x²-4x-21
y=-5x-22

==>x²-4x-21=-5x-22
==>x²+x+1=0

In R, no solution for Δ=1-4=-3<0