Question

Graph the system of linear inequalities. \(x>-2\) \(y \geq-2\) \(x \leq 1\) \(y \leq 4\)

Short answer

The solution to this system of inequalities is the region bounded by the lines \(x=-2\), \(y=-2\), \(x=1\), and \(y=4\).

Step-by-step solution

Plotting Inequality 1

The inequality \(x>-2\) implies all values of \(x\) that are greater than -2. On the number line, it is represented on the right side of the point -2. For the 2 dimensional case, draw a dashed vertical line at \(x=-2\). Since the inequality is \(x>-2\), shade to the right of this line.

Plotting Inequality 2

The inequality \(y \geq -2\) implies that all values of \(y\) are greater than or equal to -2. Hence, draw a solid horizontal line at \(y=-2\). Since the inequality is \(y \geq -2\), shade above this line.

Plotting Inequality 3

The inequality \(x \leq 1\) implies that \(x\) is less than or equal to 1. Hence, draw a solid vertical line at \(x=1\). Since the inequality is \(x \leq 1\), shade to the left of this line.

Plotting Inequality 4

The inequality \(y \leq 4\) implies that \(y\) is less than or equal to 4. Hence, draw a solid horizontal line at \(y=4\). Since the inequality is \(y \leq 4\), shade below this line.

Intersection of All Inequalities

The overlap of the shaded regions from each inequality will give the solution region to our system. This is the region that satisfies all four inequalities simultaneously.