Question

Select the point that is a solution to the system if inequalities yx^2-6

Answer 1

The correct answer is A.

`A(0,-2)`

Explanation:

Method 1

You just have to plot each point on the graph.

The one that falls within the solution region is the correct choice.

From the graph,
`A(0,-2)` falls within the solution region.

See graph

Method 2

If you substitute the points into the inequalities, the only point that will satisfy both inequalities simultaneously is A.

The first inequality is

`y\:<x^2+2`

If we substitute
`A(0,-2)`, we get;

`-2\:<\:(0)^2+2`

`-2\:<\:2`

This statement is true.

The second inequality is

`y\:>\:x^2-6`

If we substitute
`A(0,-2)`, we get;

`-2\:>\:(0)^2-6`

This gives,

`-2\:>\:-6`

This statement is also true.