**Problem 10:****Question:**Using the graph below, determine if (0, 0) is a viable solution to the system of inequalities. Explain why or why not.**Inequalities:**1. $ y > x $2. $ x > -2 $**Graph Description:**The graph includes the x and y axes with various regions shaded. The shaded regions represent the solutions to the inequalities. There are three distinct regions:- The red region indicates where $ y > x $.- The blue region indicates where $ x > -2 $.- The purple region, formed by the overlap of the red and blue regions, indicates where both inequalities are satisfied.The axes intersect at the origin (0, 0), which is marked as a reference point on the graph.**Multiple Choice Options:**- $ \text{○ No, because the point falls on the origin.} $- $ \text{○ Yes, because the point falls on a line.} $- $ \text{○ No, because the point does not fall in the area in which the shading overlaps.} $- $ \text{○ Yes, because } 0 \geq -2. $**Analysis:**The point (0, 0) is at the origin. It does not fall in the overlapping shaded region (purple), which represents the solution set for both inequalities. Thus, while the second inequality $ x > -2 $ holds true ($ 0 > -2 $), the first inequality $ y > x $ is not satisfied because $ 0 \not> 0 $.**Correct Answer:**$ \text{○ No, because the point does not fall in the area in which the shading overlaps.} $ **Scenario Description:**Billy is a landscaper and charges a flat rate of $30 per day for mowing ($x$ represents the number of days) plus $10 per hour ($y$ represents the number of hours) for any additional landscaping for a customer. He estimates that, in total, he must charge the customer more than $3,000 for the year.Aaron is also a landscaper and charges a flat rate of $25 per day of mowing ($x$ represents the number of days) plus $12 per hour ($y$ represents the number of hours) for any additional landscaping. Additionally, Aaron estimates that the customer must spend no more than $4,900 for the year.This situation is represented by the system of inequalities graphed below.**Graph Explanation:**- The graph has a standard coordinate plane with two axes ($x$ and $y$).- The shaded region on the graph represents the solutions to a system of linear inequalities.- The blue shaded area represents a constraint with a diagonal boundary line indicating a possible limitation or requirement.- The pink shaded area represents another constraint.**Multiple-choice Statements:**1. The constraint that represents Aaron's estimate is $25x + 12y \leq 4900$.2. The point $(500, 500)$ is not a solution to both inequalities.3. The point $(100, 100)$ is a solution to both inequalities.4. The constraint that represents Billy's estimate is $30x + 10y < 3000$.**Question:**Which of the following statements is not true?

10. Using the graph below, determine if (0, 0) is a viable solution to the system of inequalities. Explain why or why not. y > x x > -2 No, because the point falls on the origin. Yes, because the point falls on a line. No, because the point does not fall in the area in which the shading overlaps. Yes, because 0> -2.

10. Using the graph below, determine if (0, 0) is a viable solution to the system of inequalities. Explain why or why not. y > x x > -2 No, because the point falls on the origin. Yes, because the point falls on a line. No, because the point does not fall in the area in which the shading overlaps. Yes, because 0> -2.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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