# Two Variables Inequalities

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Two-Variable Inequalities Luz Perez MAT222: Intermediate Algebra Instructor: Francis DiFonzo Today I will be putting into words an equation on a graph that I will be working on from our textbook. The equation is on the page 539 and it is problem #68. The following equation goes like this: Shipping restrictions. The accompanying graph shows all of the possibilities for the number of refrigerators and the number of TVs that will fit into an 18-wheeler. a. Write an inequality to describe this region. b. Will the truck hold 71 refrigerators and 118 TVs? c. Will the truck hold 51 refrigerators and 176 TVs? For the first part, I will write an inequality to describe this region. We need to find the slope: m=y1-y2=330-0/0-110=-330/110=-3 x1-x2 The slope is 3/1 or -3y-y1=p(x-x1) I will use the point-slope form. y-330=-3/1(x-0) then I will substitute the point (0,330) y=-3x/1+330 we then add 300 to both sides -3x/1+330=y expression switched by placing the y on the right hand side -3x/-3=y/-3-330/-3 We divide each equation by -3 and cancel out the like terms -3y=1x+110 -3y+1x&lt;110 For the second part, ‘will the truck hold 71 refrigerators and 119 TVs? In other words, the point (71,118) in the solution region. We will use this test point in order to determine if our solution is correct by checking if the correct side of the line is shaded. In order to check it, we need to substitute the pair into the inequality and find out if it will remain correct. -3(71)+1(118)&lt;110 -213+118&lt;110 -95&lt;110. The answer would be, no, the truck will not be able to hold 71 refrigerators and 118 TVs. For the final section: Will the truck hold 51 refrigerators and 176 TVs? -3(51)+1(176)&lt;110 23&lt;110. The final answer is: yes, the