Question

solve the system of two linear inequalities graphically.\

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

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step 1 of 3 : graph the solution set of the first linear inequality.

Explanation:

Step1: Rewrite inequality to slope-intercept

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

Step2: Identify boundary line

The boundary is the line $y = \frac{6}{5}x + 6$. Since the inequality is $>$, use a dashed line.

Step3: Test a point for shading

Test $(0,0)$: $0 > \frac{6}{5}(0) + 6$ → $0 > 6$, which is false. Shade the region above the dashed line.

Step4: Graph second inequality boundary

The boundary for $y > 2$ is the horizontal dashed line $y=2$.

Step5: Shade second inequality region

Test $(0,0)$: $0 > 2$ is false. Shade the region above the dashed line $y=2$.

Step6: Find overlapping shaded region

The solution is the area that is shaded for both inequalities: above both $y = \frac{6}{5}x + 6$ and $y=2$.

Answer:

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

• Boundary line 1: Dashed line $y = \frac{6}{5}x + 6$, shade above it
• Boundary line 2: Dashed horizontal line $y=2$, shade above it
• The intersection of these two shaded areas is the solution set.