Question

How should you modify the graph to show the solution to the system of inequalities below? Check all that apply.

Shade above 2x + y = 4.

Shade below 2x + y = 4.

Shade above 2y = 6 – 2x.

Shade below 2y = 6 – 2x.

Make the boundary line 2x + y = 4 dashed.

Answer 1

1. Shade above 2x+y=4

4. Shade below 2y=6-2x

5. Make the boundary line 2x+y=4 dashed

Answer 2

Shade above 2x + y = 4,

Shade below 2y = 6 – 2x,

Make the boundary line 2x + y = 4 dashed.

Explanation:

Given system of inequalities,

2x + y > 4

2y ≤ 6 - 2x,

2(0) + (0) > 4 ( False )

i.e. Inequality 2x + y > 4 does not contain the origin,

∴ The region above 2x+y = 4 will be shaded( related equation of 2x + y > 4, blue line in the given graph )

While, 2(0) ≤ 6- 2(0),

i.e. inequality 2y ≤ 6 - 2x contains the origin,

∴ Region below 2y = 6 - 2x will be shaded ( Related equation of 2y ≤ 6 - 2x, Shown by yellow line in the graph )

Now, '>' sign shows the dotted line,

Thus, we have to make the boundary line 2x + y = 4 dashed.

Also, '≤' shows solid line. ( already shown in the diagram )