Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}5y - 6x > 30\\\\y > 2\\end{cases}$$

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

Explanation:

Step1: Rewrite first inequality to slope-intercept form

Rearrange $5y - 6x > 30$ to isolate $y$:
$5y > 6x + 30$
$y > \frac{6}{5}x + 6$

Step2: Identify boundary lines

• For $y > \frac{6}{5}x + 6$: Boundary is $y = \frac{6}{5}x + 6$ (dashed line, since inequality is $>$).
• For $y > 2$: Boundary is $y = 2$ (dashed line, since inequality is $>$).

Step3: Shade solution regions

• For $y > \frac{6}{5}x + 6$: Shade above the dashed line $y = \frac{6}{5}x + 6$.
• For $y > 2$: Shade above the dashed horizontal line $y = 2$.

Step4: Find overlapping shaded area

The solution set is the region that is shaded for both inequalities (the intersection of the two shaded areas).

Answer:

The solution set is the overlapping region above both the dashed line $y = \frac{6}{5}x + 6$ and the dashed horizontal line $y = 2$.

• Plot the dashed line $y = \frac{6}{5}x + 6$ (y-intercept at $(0,6)$, slope $\frac{6}{5}$)
• Plot the dashed horizontal line $y = 2$
• Shade the area that lies above both dashed lines.