How many solutions does this system of equations have? y=x^2+x+3
y=-2x-5

A.
no solution
B.
1 solution
C.
2 solutions
D.
3 solutions

A. No solution

Step-by-step explanation:

System of Equations

We have this system of equations:

To solve the system, we can substitute y from one equation into the other:

Prepare the second-degree equation. Adding 2x+5:

Simplifying:

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:

Since the discriminant is negative, the equation has no real solutions, thus the system of equations has no real solution.

A. No solution