Question

solve the system of two linear inequalities graphically. \\(\

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

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

Explanation:

Step1: Graph boundary lines

• For $x > -7$: Draw a dashed vertical line at $x=-7$ (dashed because the inequality is strict, not inclusive).
• For $y \geq 7$: Draw a solid horizontal line at $y=7$ (solid because the inequality includes equality).

Step2: Shade solution regions

• For $x > -7$: Shade all areas to the right of the dashed line $x=-7$.
• For $y \geq 7$: Shade all areas above and on the solid line $y=7$.

Step3: Identify overlapping region

The solution set is the intersection of the two shaded regions: all points where $x$ is greater than -7 AND $y$ is 7 or greater.

Answer:

The solution set is the region to the right of the dashed vertical line $x=-7$ and above (including the line) the solid horizontal line $y=7$. This overlapping area represents all points $(x,y)$ that satisfy both inequalities simultaneously.