In order to solve a system of inequalities, we need to find a set of all the possible values of the variable that satisfy all the original inequalities. Such set is the intersection of the solutions of each inequality.

It's easier to keep in mind the graphical interpretation on a number line:

1. The first inequality,

*x*² > 4, results in:

*x* > 2 OR

*x* < -2.

The solution is the red crosshatched region.

2. The second inequality, -1 <

*x* < 3, results in:

-1 <

*x* AND

*x* < 3.

The solution to this inequality is the blue crosshatched region.

Therefore the solution of the system is the intersection:

2 <

*x* < 3