Question

100 Points
How many solutions does this system of equations have?

Answer 1

• A) No real solutions

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Given system:

• y = x² + x + 3
• y = - 2x - 5

Equate the right sides to get a quadratic equation:

• x² + x + 3 = - 2x - 5
• x² + 3x + 8 = 0

The discriminant of ax² + bx + c = 0 is D = b² - 4ac.

Substitute a = 1, b = 3, c = 8 and find the value of D:

• D = 3² - 4*1*8 = 9 - 32 = - 23

Since D < 0, there is no real solution, hence the correct choice is A.