Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}y \\leq -5x - 10 \\\\ y > x + 2\\end{cases}$$

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

Explanation:

Step1: Identify boundary line

The boundary of $y \leq -5x -10$ is the line $y = -5x -10$. Since the inequality is $\leq$, the line will be solid.

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: Test a point for shading

Use the test point $(0,0)$:
$0 \leq -5(0) -10$
$0 \leq -10$, which is false. Shade the half-plane that does NOT contain $(0,0)$ (below the solid line).

Answer:

1. Draw a solid line through the points $(-2, 0)$ and $(0, -10)$ (this is $y=-5x-10$).
2. Shade the region below this solid line to represent the solution set of $y \leq -5x -10$.