Question

solve the system of two linear inequalities graphically.\

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

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

Explanation:

Step1: Rewrite in 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: Graph the boundary line

The boundary is $y = -\frac{2}{3}x - 6$, a straight line with slope $-\frac{2}{3}$ and y-intercept $(0, -6)$. Draw it as a dashed line (since the inequality is $<$, not $\leq$).

Step3: Shade the solution region

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

Answer:

Graph the dashed line $y = -\frac{2}{3}x - 6$, then shade the region below this line.