Two-Variable Linear Inequalities

Question 1

Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr for lawn care and $10/hr to walk dogs. Let x represent the hours he spends on lawn care and y represent the hours he spends walking dogs. Which inequality represents this situation?

Revolt · Accepted Answer

Answer image: //media.edgenuity.com/EVresources/3111-02-11-25-01-task/mc001-4.jpg

Question 2

If Ezra works less than or equal to 50 hours doing lawn care, he must spend at least hours walking dogs.

Revolt · Accepted Answer

35

Question 3

Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: .Is (60, 20) a solution? How do you know? What does this point represent?

Revolt · Accepted Answer

Yes, (60, 20) is a solution. When you substitute the values into the inequality, 15(60) + 10(20) ≥ 1100 becomes 900 + 200 ≥ 1100, or 1100 ≥ 1100. Since this is a true statement, the point is a solution. This point represents Ezra working 60 hours mowing lawns and 20 hours walking dogs, which earns him exactly the $1,100 he needs for the laptop.

Question 4

Which of the following did you include in your solution?

Revolt · Accepted Answer

The coordinate pair (60, 20) is a solution because Ezra earns 60 x $15 = $900 mowing lawns and 20 x $10 = $200 walking dogs, for a total of $1100.

Question 5

Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: Explain how to graph the solution set.

Revolt · Accepted Answer

Graph the solid boundary line 15x + 10y = 1100 through (1100/15, 0) and (0, 110). Shade the region on or above the line in the first quadrant, where 15x + 10y ≥ 1100.

Question 6

Which of the following did you include in your solution?

Revolt · Accepted Answer

Graph the boundary line using the related equation, y = –1.5x + 110.

Question 7

=✔ ><=

Revolt · Accepted Answer

✔ >

Question 8

To see how the solution set changes, suppose the coordinate pair (a, b) satisfies the original inequality. If a stays the same, b must be less thanequal to✔ greater than its previous value to satisfy the new inequality.

Revolt · Accepted Answer

✔ greater than

Question 9

Now suppose b stays the same. Then, a must be less thanequal to✔ greater than its previous value to satisfy the new inequality.

Revolt · Accepted Answer

✔ greater than

Question 10

How is the graph of the solution affected?

Revolt · Accepted Answer

The boundary line becomes dashed.; The shading switches to the other side of the boundary line.

Two-Variable Linear Inequalities Answers

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