Question 1

Consider the system of inequalities represented in the first image. Which of the following systems best describes the shaded region?

Accepted Answer

$$x - 4y  3$$

Question 2

The shaded region in the second and third images represents the solution set to a system involving a quadratic and a linear function. Which system of inequalities is shown?

Accepted Answer

$$x^2 + 2y$$ \leq 4$$ and y$$ \geq x - 3$$

Question 3

In the first image, what is the best description of the solution region?

Accepted Answer

The region where both inequalities are satisfied, above the line $$4x + y = 3$$ and below the line $$x - 4y = 3.$$

Question 4

For the system represented in the second and third images, which of the following points is in the solution set?

Accepted Answer

$$(0, -2)$$

Question 5

Which of the following best describes the boundary of the shaded region in the first image?

Accepted Answer

It is bounded by the lines $$x - 4y = 3$$ and $$4x + y = 3.$$

Question 6

If the system in the second image is changed to $$x^2 + 2y$$ \u003e 4$$ and y$$ \u003c x - 3$$, what happens to the solution region?

Accepted Answer

The solution region moves outside the parabola and below the line.

Question 7

Which of the following statements is true about the intersection of the boundaries in the first image?

Accepted Answer

The intersection point of $$x - 4y = 3$$ and $$4x + y = 3 is a $$vertex of the solution region.

Question 8

For the system $$x^2 + 2y$$ \leq 4$$ and y$$ \geq x - 3$$, what is the shape of the solution region?

Accepted Answer

A region bounded below by a line and above by a parabola.

Question 9

Suppose you want to find the area of the solution region in the second image. Which method would be most appropriate?

Accepted Answer

Set up a definite integral with limits determined by the intersection points of the parabola and the line.

Question 10

If the inequality $$x^2 + 2y$$ \leq 4$$ in the second image is replaced with x^2$ + 2y \geq 4$$, how does the solution region change?

Accepted Answer

The solution region is now outside the parabola and above the line.

Graphing Solution Sets for Systems of Inequalities

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