Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}2x + 8y < -8 \\\\ x \\geq 5\\end{cases}$$

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

Explanation:

Step1: Rewrite in slope-intercept form

Rearrange $2x + 8y < -8$ to solve for $y$:
$8y < -2x -8$
$y < -\frac{2}{8}x - \frac{8}{8}$
$y < -\frac{1}{4}x - 1$

Step2: Identify boundary line type

Since the inequality is $<$ (not $\leq$), the boundary line $y = -\frac{1}{4}x - 1$ is dashed.

Step3: Test a point for shading

Use the origin $(0,0)$:
$0 < -\frac{1}{4}(0) - 1$ simplifies to $0 < -1$, which is false. Shade the half-plane not containing the origin.

Answer:

Graph a dashed line with slope $-\frac{1}{4}$ and y-intercept $(0, -1)$, then shade the region below/left of this line (the region that does not include the point $(0,0)$).