Question

solve the system of two linear inequalities graphically. \

$$\begin{cases} y < 6 \\\\ y \\geq 2 \\end{cases}$$

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

Explanation:

Step1: Graph boundary $y=6$

Draw a dashed horizontal line at $y=6$ (dashed because $y<6$ does not include equality).

Step2: Graph boundary $y=2$

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

Step3: Shade overlapping solution region

Shade the area between the two lines: above the solid line $y=2$ and below the dashed line $y=6$.

Answer:

The solution set is the shaded region where $2\leq y < 6$, represented by a solid horizontal line at $y=2$, a dashed horizontal line at $y=6$, and the area between them filled in.