Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}x > 2 \\\\ y \\geq 4\\end{cases}$$

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

Explanation:

Step1: Graph boundary $x=2$

Draw a dashed vertical line at $x=2$ (dashed because $x>2$ does not include equality).

Step2: Shade region for $x>2$

Shade all areas to the right of the line $x=2$.

Step3: Graph boundary $y=4$

Draw a solid horizontal line at $y=4$ (solid because $y\geq4$ includes equality).

Step4: Shade region for $y\geq4$

Shade all areas above and including the line $y=4$.

Step5: Identify overlapping region

The solution set is the intersection of the two shaded regions: the area to the right of $x=2$ and above/on $y=4$.

Answer:

The solution set is the region that is to the right of the dashed line $x=2$ and above or on the solid line $y=4$. Visually, this is the top-right quadrant-like area bounded by these two lines.