Mathematics: Which system of linear inequalities is graphed?

None of them have perpendicular lines except for the blue one if I am seeing right....

Which system of linear inequalities is graphed?

windmadness5331

11.03.2022

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.

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