Solving Two - Variable Inequalities

Solving Two- Variable Inequalities

This week our lesson was solving two variable inequalities that apply to practical situations. We were given a set graph of objects to be shipped together in the same 18- wheeler and we had to determine based on the purchasing company if we would be able to ship the about asked together. The graphs show the different range of answers that would work in the given solution.

The problem we were asked to solve is on page 539 problem 68 (Dugopolski, 2012) . The 18-wheeler can carry a maximum of 330 TV's and no refrigerators, or maximum of no TV's and 110 refrigerators. Here is the graph used for this problem: Pretend the triangle region is shaded in, write an inequality describing this region.

The graph is showing the number of Refrigerators on the x axis and the number os TV's on the y axis, the points on the graph, (0,330) and (110,0) are given so we can determine the slope of this line. We will do this by using slope form:

330-0= - 3__ Point slope form

110-0 1 The slope is -3/1

We can now use the point slope form of a linear equation. Here we will now show the steps of our linear inequality. Start with point-slope form:

Substitute the slope for m and (333,0) for x and y.

y-330=-3/1 (x-0) Use the distributive property and add 330 to both side

+330 +330

(1)y=-3/1x+33(1) Multiply both sides by 1

(+3x)y=-3x+330(+3x) Add 3x to both sides to cancel out like terms

3x+y< 330 Final Inequality

The graph has a solid line rather than a dashed line stating the points on the line are part of a solution. I will use a solid line every time I see a equal to sign.

The next two parts of the question are what we call a test point to see if the points given prove the inequality to be true.

1. Will the truck hold 71 refrigerators and 118 TVs? To solve this question the order pair is to be substituted into the inequality we previously created, if the statement is true the combination of refrigerators and TVs will work and remain in the shaded portion of the graph above.

3x+y < 330 Linear Inequality

3(71) + 118< 330 Substitute x and y values

213+118 < 330

331 < 330 False statement the truck will not hold the amount given.

2.Will the truck hold 51 refrigerators and 176 TVs?

3x+y < 330 Solve this problem