Question

question 4 of 10, step 1 of 3
solve the system of two linear inequalities graphically.
step 1 of 3: graph the solution set of the first linear inequality.
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$$\begin{cases} y \\leq -2x + 3 \\\\ y > 6x - 9 \\end{cases}$$

Explanation:

Step1: Identify boundary line (first inequality)

The first inequality is $y > 6x - 9$. Its boundary is the line $y = 6x - 9$. Since the inequality uses $>$, the line is dashed (points on the line are not included).

Step2: Find intercepts for boundary line

• x-intercept: Set $y=0$, solve $0 = 6x - 9$

$6x = 9 \implies x = \frac{9}{6} = \frac{3}{2}$
Intercept: $(\frac{3}{2}, 0)$

• y-intercept: Set $x=0$, solve $y = 6(0) - 9$

$y = -9$
Intercept: $(0, -9)$

Step3: Test a point to shade region

Use the test point $(0,0)$:
$0 > 6(0) - 9 \implies 0 > -9$, which is true.
Shade the region above the dashed line $y=6x-9$.

Answer:

Graph the dashed line $y=6x-9$ (passing through $(\frac{3}{2}, 0)$ and $(0, -9)$), then shade the region above this line.