Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}-2y < 5x - 15\\\\-5y \\geq -6x + 45\\end{cases}$$

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step 2 of 3 : graph the solution set of the second linear inequality.

Explanation:

Step1: Isolate y in the inequality

Start with the second inequality:
$-5y \geq -6x + 45$
Divide all terms by $-5$, reversing the inequality sign:
$y \leq \frac{6}{5}x - 9$

Step2: Identify boundary line

The boundary line is the equality $y = \frac{6}{5}x - 9$. Since the inequality is $\leq$, the line is solid (includes the line itself).

Step3: Determine shaded region

Test the point $(0,0)$ in the simplified inequality:
$0 \leq \frac{6}{5}(0) - 9$
$0 \leq -9$, which is false. So we shade the region below the solid boundary line.

Answer:

1. Draw the solid boundary line $y = \frac{6}{5}x - 9$ (this line has a y-intercept at $(0, -9)$ and a slope of $\frac{6}{5}$).
2. Shade the entire region that lies below this solid line. This shaded area represents the solution set of the second inequality.