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

Step-by-step explanation:

y=-3x²-4x+7 ... (*)

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

use (*) put the value of y in (**):

3x + 2 (-3x²-4x+7) = 18

3x-6x²-8x + 14 - 18 = 0

-6x²-5x - 4 = 0

6x²+5x+4 = 0

delta = b² - 4ac a = 6 b=5 c = 4

delta = 5² - 4 (6) (4) = 25 - 96 = - 71 negatif

so no reals solution