Question

solve the system of two linear inequalities graphically.\

$$\begin{cases} y < -5x - 10 \\\\ 4y \\geq 4x + 32 \\end{cases}$$

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

Explanation:

Step1: Identify boundary line

The first inequality is $y < -5x - 10$. Its boundary is the line $y = -5x - 10$. Since the inequality uses $<$, the line is dashed.

Step2: Find intercepts for plotting

• x-intercept: Set $y=0$:

$0 = -5x - 10$
$5x = -10$
$x = -2$
So the x-intercept is $(-2, 0)$.

• y-intercept: Set $x=0$:

$y = -5(0) - 10 = -10$
So the y-intercept is $(0, -10)$.

Step3: Determine shaded region

Test the origin $(0,0)$ in $y < -5x -10$:
$0 < -5(0) -10$ → $0 < -10$, which is false. Shade the region not containing the origin (below the dashed line).

Answer:

Graph a dashed line passing through $(-2, 0)$ and $(0, -10)$, then shade the region below this line.