Question

given which of the following describes the boundary line and shading for the second inequality in the system

Answer 1

Solid Line, Shade Above

Explanation:

Given:

`\left\{\begin{array}{l} y<-2 x+3 \\ y \geq x-4 \end{array}\right.`

The second inequality in the system is:

`y\geq x-4`

The intercepts of the boundary line (y=x-4) are (0, -4) and (4,0).

Since the inequality has an equal to sign attached, we use a solid line.

At (0,0)

`\begin{gathered} y\geq x-4 \\ 0\geq-4 \end{gathered}`

Since the inequality 0≥-4 is true, shade the side that contains (0, 0) as shown in the graph below:

So, we use a solid line and shade above the boundary line.