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,
\(\sqrt{1^2-4*1*1} \geq 0\)
\(\sqrt{1-4} \geq 0\)
\(\sqrt{-3}
geq 0\)
Therefore, our given system has no solutions and option D is the correct choices.
