Question

solve the system of two linear inequalities graphically.\

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

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

Explanation:

Step1: Rewrite first inequality to slope-intercept form

Isolate $y$ in $4x + 6y < -36$:

$$\begin{align*} 6y &< -4x - 36\\ y &< -\frac{2}{3}x - 6 \end{align*}$$

Step2: Identify boundary lines

1. For $y < -\frac{2}{3}x - 6$: Boundary is dashed line $y = -\frac{2}{3}x - 6$ (since inequality is strict). Shade below this line.
2. For $x \geq -4$: Boundary is solid vertical line $x = -4$. Shade to the right of this line.

Step3: Find overlapping shaded region

The solution set is the area that is shaded both below $y = -\frac{2}{3}x - 6$ and to the right of $x = -4$.

Answer:

The graph consists of:

1. A dashed line $y = -\frac{2}{3}x - 6$, with shading below the line.
2. A solid vertical line $x = -4$, with shading to the right of the line.
3. The overlapping shaded region (below the dashed line and right of the solid line) is the solution set for the system.