Question

Which system of linear inequalities is graphed?

Answer 1

To determine the system of inequality that has been graphed, we need to be very smart.

Observe that all the equations are the same.

Also note that all the lines are solid. This should tell you that the inequities should involve.

`\ge \:or\: \le`

Therefore the answer is between option A and B.

So we choose a point in the solution region to discriminate between A and B.

Let us choose the origin since that is easy to evaluate.

We substitute into option A to get.

`y\le 3x-1\:and\: x+ 3y \ge 6`

`0\le 3(0)-1\:and\: 0+ 3(0) \ge 6`

`0\le -1\:and\: 0\ge 6`

The above statements are false

We now substitute into option B

`y\ge 3x-1\:and\: x+ 3y \le 6`

`0\ge 3(0)-1\:and\: 0+ 3(0) \le 6`

`0\ge-1\:and\: 0 \le 6`

Both statements are true, therefore the correct answer is option B.