Two Variable Inequalities

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Two Variable Inequalities
Two Variable Inequalities
Melissa Hillard
MAT222: Intermediate Algebra (GSQ1331C)
Instructor Lisa Wallace
August 10, 2013

Two Variable Inequalities For this assignment the class was asked to solve problem 68 from page 539 of our textbook Elementary and intermediate algebra (Dugopolski, 2012). Problem 68 tells the number of refrigerators and TV’s that will fit inside of an 18 wheeler truck. The class is asked to write an inequality to describe the region of the graph that is shaded in based upon these numbers. The class is then asked to solve a combination of problems to determine how many refrigerators and TV the 18 wheeler can hold at one time.
The graph shows the number of possibilities for the number of TV’s and refrigerators that will fit in an 18 wheeler at one time. The first thing I need to do is write an inequality to describe the shaded region of the graph. I will let X represent the refrigerators and Y the TV’s.

I know that my line is going from (0,330) to (110,0). The graph has a solid line rather than a dashed line meaning that points on the line itself are part of the solution.
I know the formula I need to use to write an inequality is y=mx+b m=y2-y1/ x2-x1 This tells me what my slope is
Y=mx+b I know that b= my y intercept, which is 330. If the lines ran parallel I would not have an intercept point.
Y=x+330 Slope intercept form.
(1)y=(1)+330(1) Multiply by 1.
Y=-3x+330
3x+y ≤330 or 3x+y-330≤0 This is the linear inequality for my line.
Now that I know what Y is I can solve the other linear equations.
The next problem asks will the truck hold 71 refrigerators and 118 TVs. I need to determine if the test points (71, 118) are within the shaded region of my graph. x=71 y=118
3(71)+118≤330
213+118≤330
331≤330 This is false. So the answer is no, the truck cannot hold 71 refrigerators and 118 TVs. The graph would now have a horizontal line at y=118

References: Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing. http://www.aleks.com

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