Question

Solve the Linear-Quadratic System of Inequalities. Shade the solution on the graph provided.

Answer 1

Answer:

We have the system:

y > x^2 - 1

y < (-1/2)*x + 3

To find the solutions of this set we need to graph the solutions range of both sets, and see the intersection between these solution ranges.

How we do it?

Start with the first one.

First, we graph the equation:

y = x^2 - 1

Now because we are using the symbol ">" means that y is smaller than the thing at the right, then the graph of the equation will be with a dashed line (which means that the points on the line are not solutions) and we will shade all the region above the line

For the other inequality we do the same:

First we graph:

y = (-1/2)*x + 3

And because we have the symbol "<" we again use a dashed line, but this time we will shade all the region below the line.

Once we shaded both regions, the region where we have both shades will be the region of solutions for the system of inequalities.

You can see the graph below.