Question

Which graph represents the following system of inequalities?

Answer 1

D

Explanation:

On graphing the 3 equations, we find that the central area (triangle) formed by the 3 inequalities is the solution.

Answer 2

D

Explanation:

When graphing inequalities:

• < or > : dashed lines
• ≤ or ≥ : solid line
• < or ≤ : shading under the line
• > or ≥ : shading above the line

Given inequalities:

`\begin{cases}y > (1)/(2)x-1\\\\y\leq -x+1\\\\y > -2x-1 \end{cases}`

From inspection of the given graphs, the red dashed line is the first inequality as it is the only inequality with a positive slope.

The blue sold line is the second inequality, as it is the only inequality with the sign that suggest a solid line.

Therefore, by process of elimination, the green dashed line is the third inequality.

Using the inequality signs and their definitions for shading, find the graph that has:

• Shading above the red dashed line
• Shading below the blue solid line
• Shading above the green dashed line

The only graph that matches these conditions is graph D