Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}2x + 6y < -12\\\\x \\geq 2\\end{cases}$$

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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 $2x + 6y < -12$ to solve for $y$:
$6y < -2x -12$
$y < -\frac{1}{3}x - 2$

Step2: Graph the boundary line

Plot the line $y = -\frac{1}{3}x - 2$ as a dashed line (since the inequality is $<$, not $\leq$). The y-intercept is $(0, -2)$, and using the slope $-\frac{1}{3}$, another point is $(3, -3)$.

Step3: Shade the solution region

Since $y < -\frac{1}{3}x - 2$, shade the area below the dashed boundary line.

Answer:

The graph of $2x + 6y < -12$ is a dashed line $y = -\frac{1}{3}x - 2$ with the region below the line shaded.