Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}x > -7 \\\\ y \\geq 7\\end{cases}$$

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step 3 of 3 : graph the solution set for the system.\
answer

Explanation:

Step1: Graph boundary $x=-7$

Draw a dashed vertical line at $x=-7$ (dashed because the inequality is $x > -7$, so the line itself is not part of the solution). Shade the region to the right of this line (all points where $x$ is greater than -7).

Step2: Graph boundary $y=7$

Draw a solid horizontal line at $y=7$ (solid because the inequality is $y \geq 7$, so the line itself is part of the solution). Shade the region above this line (all points where $y$ is 7 or greater).

Step3: Identify overlapping region

The solution set is the intersection of the two shaded regions: all points to the right of $x=-7$ (dashed line) and above or on $y=7$ (solid line).

Answer:

The solution is the region that is:

1. To the right of the dashed vertical line $x=-7$
2. Above or on the solid horizontal line $y=7$

The overlapping shaded area represents all $(x,y)$ pairs that satisfy both inequalities.