Answer
$(-2, 14)$ and $(4,-4)$
Work Step by Step
We can solve the system of equation using the graphical method and then confirm with algebraic operations.
(a) Graphical method: read the coordinates of the intersection points of the line and the parabola, we get $(-2, 14)$ and $(4,-4)$ which are the solutions to the system.
(b) Confirm with algebraic operations:
Step 1. Use substitution method: from equation 1, we get $y=8-3x$
Step 2. Substitute it in the second equation to get $x^2-5x=8-3x$ or $x^2-2x-8=0$
Step 3. Factor the above equation to get $(x-4)(x+2)=0$ which gives $x=-2, 4$
Step 4. Back-substitute the results in the first equation to get $x=-2, y=14$ and $x=4, y=-4$
Step 5. The solutions to the system are $(-2, 14)$ and $(4,-4)$
