Question

solve the system of two linear inequalities graphically.
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$$\begin{cases} x > -7 \\\\ y \\geq -1 \\end{cases}$$

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

Explanation:

Step1: Graph boundary $x=-7$

Draw a dashed vertical line at $x=-7$ (dashed because $x>-7$ does not include equality). Shade the region to the right of this line, since $x$ values greater than $-7$ lie here.

Step2: Graph boundary $y=-1$

Draw a solid horizontal line at $y=-1$ (solid because $y\geq-1$ includes equality). Shade the region above this line, since $y$ values greater than or equal to $-1$ lie here.

Step3: Identify overlapping shaded region

The solution set is the intersection of the two shaded regions: the area to the right of $x=-7$ and above or on $y=-1$.

Answer:

The solution set is the region bounded by the dashed vertical line $x=-7$ (right side) and solid horizontal line $y=-1$ (above/on the line), where the two shaded areas overlap.

• Dashed line: $x=-7$, shade right
• Solid line: $y=-1$, shade above
• Overlap is the final solution region