Question

question 14
graph the system
$\

$$\begin{cases} y \\leq -\\frac{4}{3}x + 1 \\\\ y < \\frac{5}{2}x + 2 \\end{cases}$$

$
this system of inequalities select an answer
clear all draw:
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Explanation:

Step1: Graph boundary of first inequality

First, identify the boundary line $y = -\frac{4}{3}x + 1$. This is a solid line because the inequality is $\leq$ (includes the boundary).

• Find intercepts:
• When $x=0$, $y=1$ (y-intercept: $(0,1)$)
• When $y=0$, $0 = -\frac{4}{3}x +1 \implies x = \frac{3}{4}$ (x-intercept: $(\frac{3}{4},0)$)

Shade the region below this line, since $y$ is less than or equal to the expression.

Step2: Graph boundary of second inequality

Next, identify the boundary line $y = \frac{5}{2}x + 2$. This is a dashed line because the inequality is $<$ (does not include the boundary).

• Find intercepts:
• When $x=0$, $y=2$ (y-intercept: $(0,2)$)
• When $y=0$, $0 = \frac{5}{2}x +2 \implies x = -\frac{4}{5}$ (x-intercept: $(-\frac{4}{5},0)$)

Shade the region below this dashed line, since $y$ is less than the expression.

Step3: Identify overlapping region

The solution to the system is the area where the two shaded regions overlap.

Answer:

1. Draw a solid line through $(0,1)$ and $(\frac{3}{4}, 0)$, shade below it.
2. Draw a dashed line through $(0,2)$ and $(-\frac{4}{5}, 0)$, shade below it.
3. The overlapping shaded area is the solution set.