Two- Variable Inequalities

In Elementary Algebra we have learned how to forge systems of equations. The solution to a system of linear equations is the point where the graphical records of the lines intersect. The solution to a system of linear inequalities is every point in a region of the graph where the inequalities overlap, rather than the point of intersection of the lines (Slavin, 2001).This week assignment required to solve problem 68 on page 539 (Dugopolski, 2012). I lead be giving a precise presentation on math required for the solution to this problem the accompanying graph shows all of the possibilities for the recite of refrigerators and the add up of TVs that will fit into an 18-wheeler. The point-slope form of a linear equation to write the equation itself batch now be designd. These be the steps we take to solve our linear disagreement. I will make with the point-slope form. Substitute slope form with (300, 0) for the x and y. Next we are going to use the distributive property and th en add 330 to both sides and divided both sides by -3 and cancel out same terms.The graph has a solid line rather than a dashed line indicating that points on the line itself are part of the solution set. This will be true anytime the dissimilitude symbol has the equal to bar.a) Write an inequality to describe this region.p = y1-y2 /x1-x2 = 330 0 / 0-one hundred ten = -3/1 the slope is -3/1 or -3 y y1 = p(x x1) y 330 = 3 / 1(x-0) y= 3x/1 + 330 -3x/1 +330 = y expression switch by place the y on the pay off hand side -3x/-3 = y/-3 330/ -3 divide each equation by -3 and cancel out like terms -3y = 1x + 110 -3y + 1x 110b) exit the truck hold 71 refrigerators and 118 TVs? In this problem I will be substituting 71 where the y is for refrigerators and 118 where the x is for TVs to determine if the truck will hold them.-3 (71) + 1 (118) 110 -213 + 118 110 -95 110 Which means that the truck will not hold 71 refrigerators and 118 TVs.c) Will the truck hold 51 refrigerators and 176 TVs? This problem is similar to the previous one.-3 (51) + 1 (176) 110 -153 +176 110 23 110 yes, the truck will hold at least 51 refrigerators and 176 TVsThe Burbank Buy More blood is going to make an order which will include at most 60 refrigerators. What is the utmost number of TVs which could also be delivered on the same 18-wheeler? Describe the restrictions this would add to the existing graph. Solving for y1(60) + -3y 110 -3y -60 + 110 add 110 to -60 to get 50 -3y 50 divide both terms by -3 -3y/-3 50/-3 signs flip y -50/3 or y = 16There will be no added restriction because the maximum numbers of TVs The next day, the Burbank Buy More decides they will have a television sale so they change their order to include at least 200 TVs. What is the maximum number of refrigerators which could also be delivered in the same truck? Describe the restrictions this would add to the original graph. 1x + -3 (200) 110x 600 + 100 x = 710 If 200 TVs are ship.When graphing linear inequalities and they are greater than or less than you will use a dashed line. When the inequality is greater than or equal to or less than or equal to you will then use a solid line, which indicates that the points on the line are part of the solution set (Slavin, 2001). In this composition I have shown you a linear equation and broke down each step in solving the equation. I used the method of substitution for the variables and explained what the equations represent.