Question

solve the system of two linear inequalities graphically. \\(\

$$\begin{cases} 4x + 6y < -36 \\\\ x \\geq -5 \\end{cases}$$

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

Explanation:

Step1: Rewrite inequality to slope-intercept

Rearrange $4x + 6y < -36$:
$6y < -4x - 36$
$y < -\frac{2}{3}x - 6$

Step2: Graph boundary lines

1. For $y < -\frac{2}{3}x - 6$: Draw a dashed line with slope $-\frac{2}{3}$ and y-intercept $(0, -6)$.
2. For $x \geq -5$: Draw a solid vertical line at $x=-5$.

Step3: Shade solution regions

1. For $y < -\frac{2}{3}x - 6$: Shade below the dashed line.
2. For $x \geq -5$: Shade to the right of the solid vertical line.

Step4: Identify overlapping region

The solution set is the intersection of the two shaded areas: to the right of $x=-5$, below the dashed line $y = -\frac{2}{3}x - 6$.

Answer:

The solution set is the overlapping region: all points that lie to the right of the solid vertical line $x=-5$ and below the dashed line $y = -\frac{2}{3}x - 6$.

• Solid vertical line at $x=-5$, shaded right of it.
• Dashed line $y = -\frac{2}{3}x - 6$, shaded below it.
• The intersection of these shaded areas is the final solution.