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A system of inequalities is a set of two or more inequalities that are considered simultaneously.
Each inequality in the system provides a constraint on the solution.
When solving a system of inequalities, the goal is to find all the points that satisfy all the inequalities together.

In this case, we have two inequalities: \(y \leq -3\) and \(x \geq -1\).
Each inequality represents a boundary on the graph, which helps us determine the feasible region.

The solution region is the area on the graph where the shaded regions of all inequalities in a system overlap.
This region contains all the points that satisfy all of the inequalities in the system.

For the inequalities \(y \leq -3\) and \(x \geq -1\), we first graph each boundary separately.
We shade the area below the line \(y = -3\) because it includes all points where \(y\) is less than or equal to \(-3\).
Next, we shade to the right of the line \(x = -1\) which includes all points where \(x\) is greater than or equal to \(-1\).

Finally, the solution region is where these two shaded areas overlap.
It's a common area that satisfies both inequalities, representing the solution to the system.

Graphing lines is a critical step when working with systems of inequalities.
Each line represents one of the inequalities in the system.

Here's a simple guide to graphing lines for inequalities:

• For \(y \leq -3\), plot a horizontal line at \(y = -3\). Make the line solid because the inequality includes points on the line (\( \leq\) or \( \geq\)). Then, shade below the line.


• For \(x \geq -1\), plot a vertical line at \(x = -1\). Again, use a solid line, and shade to the right of the line where \(x\) values are greater than or equal to \(-1\).

Don't forget that solid lines are used when the inequality includes the boundary (\( \leq\) or \( \geq\)).
Dashed lines are used when the boundary is not included in the solution (\( < \) or \( > \)). Understanding these rules helps you accurately graph lines for inequalities.