Question

5.4.4 Practice Modeling: Two variable systems of inequalities

Answer 1

Answer:

The system has no solution, because there's no intersected areas.

Step-by-step explanation:

We have the following inequalities

$2x-3y>6$

$y \geq x^{2} -1$

This is a two variable system of inequalities, where the first one is linear (line) and the second one is quadratic (parabolla).

It's important to know that a two variable inequalitiy has ordered pairs as solution, which means its solution is an area in the coordinate system. To find such area, we just need to graph both expressions as equations:

$2x-3y=6\\y=x^{2} -1$

(First image attached)

Then, we use the inequality signs to find each area of solution, as the second image shows.

In this case, the system has no solution, because there's no intersected areas.