Question

Please help as quickly as possible (20pts)

Find the solutions to the following linear-quadratic systems algebraically. Select the ordered pair that is one of the correct solutions from among the choices below
Y=x^2+3x+8
Y=2x+10
a)(2,14)
b)(0,10)
c)(-2,6)
d)(0,8)

Answer 1

c) (-2, 6)

Explanation:

Subtracting the second equation from the first gives ...

(y) -(y) = (x^2 +3x +8) -(2x +10)

0 = x^2 +x -2 . . . . . simplify

0 = (x -1)(x +2) . . . . factor

Solutions for x are 1 and -2. The corresponding y-values are ...

y = 2{1, -2} +10 = {2, -4} +10 = {12, 6}

The solutions are (1, 12) and (-2, 6). The only matching choice is (-2, 6).