Question

Which inequality will have a solid boundary line and a shaded region above its graph?


x − y ≥ 3




2x − 3y ≤ 3




3y − x < 2




2x + y < 7

Answer 1

A solid line means either ≥ or ≤

So either A or B
 
Above the graph: Must be greater than y

Therefore, the final answer would be letter B:

2x − 3y ≤ 3 

I hope my answer has come to your help. God bless and have a nice day ahead!

Answer 2

Answer:

$2x-3y\leq 3$

Step-by-step explanation:

The first inequality $2x-3y\leq 3$ is the one that have a solid boundary line and a shaded region above its graph.

First of all, when the inequality signs are $<, >$, the boundary line isn't solid. When the inequality signs are $\leq ,\geq$, the bounday line is solid. The reason of this is because the second pair of relations involve equivalen, which refer to all solution on the boundary line.

Having said that, the possible answers are the first and second one, because they have  $\leq ,\geq$ .

Now, to know if the shaded are is above the line, we need to evaluate the expression at (0,0).

In the first inequality, we have

$x-y\geq 3\\0-0 \geq 3\\0 \geq 3$ which is false.

The second inequality

$2x-3y\leq 3\\0-0 \leq 3$ which is true.

Therefore, the second inequality has a shaded region above its line. You can chek this out in the image attached.