Answer:
Answer: A. No solution
Step-by-step explanation:
System of Equations
We have this system of equations:
[tex]y=x^2+x+3[/tex]
[tex]y=-2x-5[/tex]
To solve the system, we can substitute y from one equation into the other:
[tex]x^2+x+3=-2x-5[/tex]
Prepare the second-degree equation. Adding 2x+5:
[tex]x^2+x+3+2x+5=0[/tex]
Simplifying:
[tex]x^2+3x+8=0[/tex]
The equation has the coefficients:
a=1, b=3, c=8
To find out the number of real solutions of the quadratic equation, we calculate the discriminant d:
[tex]d=b^2-4ac[/tex]
[tex]d=3^2-4(1)(8)[/tex]
[tex]d=9-32=-23[/tex]
Since the discriminant is negative, the equation has no real solutions, thus the system of equations has no real solution.
Answer: A. No solution
