Question

solve the system of two linear inequalities graphically.\

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

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

Explanation:

Step1: Rewrite inequality to slope-intercept form

First, isolate $y$ in $4x + 6y < -36$:
Subtract $4x$ from both sides: $6y < -4x - 36$
Divide by 6: $y < -\frac{2}{3}x - 6$

Step2: Identify boundary line type

Since the inequality is $<$, use a dashed line for $y = -\frac{2}{3}x - 6$.

Step3: Determine shaded region

Test the origin $(0,0)$: $0 < -\frac{2}{3}(0) - 6$ simplifies to $0 < -6$, which is false. Shade the region below the dashed line.

Step4: Graph the second inequality (for full context)

$x \geq -4$ is a solid vertical line at $x=-4$, shaded to the right of the line.

Step5: Find overlapping solution region

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

Answer:

1. For $4x + 6y < -36$: Graph the dashed line $y = -\frac{2}{3}x - 6$, then shade the region below this line.
2. The full system solution is the overlapping area: right of $x=-4$ (solid vertical line) and below $y = -\frac{2}{3}x - 6$ (dashed line).