Answer
$(-0.5, 1.75$ and $(2, -2)$
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 two parabolas, we get $(-0.5, 1.75$ and $(2, -2)$ which are the solutions to the system.
(b) Confirm with algebraic operations:
Step 1. Add up the two equations to eliminate $y$ and get $2x^2-3x-2=0$
Step 2. Factor the above equation as $(2x+1)(x-2)=0$ which gives $x=-\frac{1}{2}, 2$
Step 3. Plug-in the numbers to get $y=2-x^2=\frac{7}{4}$ and $y=-2$
Step 4. The solutions to the system are $(-\frac{1}{2}, \frac{7}{4})$ and $(2, -2)$
