Question

y ≥ -x + 2
y < 3x - 2
solution (1,1)
write the system of inequalities represented.

Explanation:

Step1: Analyze the solid line

The solid line has a slope of -1 and y-intercept 2, so its equation is \( y = -x + 2 \). Since the shaded region is above this line, the inequality is \( y \geq -x + 2 \).

Step2: Analyze the dashed line

The dashed line has a slope of 3 and y-intercept -2, so its equation is \( y = 3x - 2 \). Since the shaded region is above this dashed line, the inequality is \( y > 3x - 2 \).

Answer:

The system of inequalities is \(

$$\begin{cases} y \geq -x + 2 \\ y > 3x - 2 \end{cases}$$

\)