Two-Variable Linear Inequalities Answers
Select all of the following ordered pairs that are solutions to the inequality.
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.
Now suppose b stays the same. Then, a must be less thanequal to✔ greater than its previous value to satisfy the new inequality.
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?
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.
Which of the following did you include in your solution?
Which of the following did you include in your solution?
=✔ ><=
How is the graph of the solution affected?
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. He currently charges in half-hour intervals. Recall the inequality that represents this situation: .Ezra decides to charge per dog instead of per hour. How does the solution set change? What are the limitations on x and y? Explain.
The solution set changes because the allowed values for y are now whole numbers, as Ezra cannot walk a fraction of a dog. Previously, y represented hours and was restricted to non-negative multiples of 0.5. The limitations on x remain the same: x must be a non-negative multiple of 0.5 because Ezra still charges by the half-hour for mowing lawns. Both variables must be non-negative because he cannot work negative hours or walk a negative number of dogs.
Which of the following did you include in your explanation?
What is a solution to the inequality? X (2, 1)(3, 0)✔ (4, 1)
Ezra works two summer jobs to save for a laptop that costs at least $1100. He considers adjusting his rates to the following:Lawn care: $250 per lawn for the summerDog walking: $300 per dog for the summerWhich inequality represents this situation?
Ezra works two summer jobs to save for a laptop that costs at least $1100. He decides to adjust his rates to $250 per lawn (x) for the summer and $300 per dog (y) for the summer, and to limit himself to 2 dogs.Describe how to find a solution graphically.
First, write the inequality 250x + 300y ≥ 1100 and graph the boundary line in the first quadrant, since the number of lawns and dogs must be non-negative. Because the laptop costs at least $1100, shade the half-plane above the line (the side that does not include the origin). Then, draw a horizontal line at y = 2 to represent the limit of 2 dogs. The solutions are the points with integer coordinates that fall within the intersection of the shaded region and the area on or below the line y = 2.
Which of the following did you include in your answer?
⇒ 1180.
60
If Ezra limits himself to 1 dog, how many lawns does he have to care for to reach his goal?
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