Question

Question #3:The system of equations below form a line and a parabola. Select all possible solutions to this system from the answer choices below.x + y = 5x^2+ y = 11(-2,7)(7,2)(5,0)(3,2)(2,3)

Answer 1

x + y = 5 -----------------------------------------(1)

$x^2+y=11-----------------(2)$

From equation (1), we have

y = 5 - x ----------------------------------------(3)

Substituting equation (3) into equation (2), we have

$\begin{gathered} x^2+(5-x)=11 \\ \Rightarrow x^2-x+5-11=0 \\ \Rightarrow x^2-x-6=0 \end{gathered}$

Therefore

$\begin{gathered} x^2+2x-3x-6^2=0 \\ x(x+2)-3(x+2)=0 \end{gathered}$

Hence

$\begin{gathered} (x-3)(x+2)=0 \\ \Rightarrow x=3\text{ or -2} \end{gathered}$

When x = 3 and using y = 5 - x

y = 5 - 3 = 2

and when x = -2

y = 5 - (-2) = 5+2=7

Therefore the possible solutions are

(3, 2) and (-2, 7)