Question

Select the correct answer.

Determine the number of solutions to the following system of equations.
y=-3x^2 - 4x +7
3x + 2y = 18

The system has three real solutions.
The system has one real solution.
The system has two real solutions.
The system has no real solutions.

Answer 1

The system has no real solutions.

Explanation:

hello :

the system is : y=-3x² - 4x +7.....(*)

3x + 2y = 18.....(**)

use (*) put tue value for y in (**) : 3x+2(-3x² - 4x +7) = 18

3x+-6x² -8x +14 = 18

-6x²-5x-4 =0

6x²+5x+4 =0

use this equation calculate : delta = 5²-4(6)(4) = -71

delta negatif :The system has no real solutions.