Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}x > 6\\\\y \\geq 2\\end{cases}$$

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

Explanation:

Step1: Graph boundary $x=6$

Draw a dashed vertical line at $x=6$ (dashed because $x>6$ does not include equality).

Step2: Shade region for $x>6$

Shade all areas to the right of the line $x=6$, since these are the points where $x$ values are greater than 6.

Step3: Graph boundary $y=2$

Draw a solid horizontal line at $y=2$ (solid because $y\geq2$ includes equality).

Step4: Shade region for $y\geq2$

Shade all areas above and on the line $y=2$, since these are the points where $y$ values are 2 or greater.

Step5: Identify overlapping region

The solution set is the intersection of the two shaded regions: all points to the right of $x=6$ and above or on $y=2$.

Answer:

The solution set is the region that is to the right of the dashed vertical line $x=6$ and above or on the solid horizontal line $y=2$. This overlapping shaded area represents all $(x,y)$ pairs that satisfy both inequalities simultaneously.