Systems of Equations and Inequalities - 2750 Words

Systems of Equations and Inequalities (Math Problem Sample) Content: MAT101 SLP 4 Answer TemplateI affirm that this assignment contains all original work. I am familiar with Trident Universityà ¢Ã¢â€š ¬s Academic Integrity policy located in the Trident Policy Handbook. I affirm that I have not engaged in direct duplication, cop/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. My name below affirms that the assignment was completed individually, and all work presented is my own.Name:Date:Instructor:Use this template to insert your answers for the assignment. Please use one of the four methods for showing Your work (EE, Math Type, ALT keys, or neatly typed). Remember that Your work should be clear and legible.Prob lems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.1. Describe the three types of solutions systems of equations have when graphed.Answer: __________________________________________________________ 1 linear equations e.g. 2a+4b=30These systems can have no solution, many solutions or a unique solution. 2 Unique solution equation e.g. (2,3,4) or A=2.B=3 ,C=4The number of variables is equal to the number of non-zero rows. 3 Infinitely many solution-It is consistent and the number of variables is more than the number Of non-zero rowse.g. (2a-2b+3c, 2a+3b-c, 7c)2. The sum of two numbers is 30 and their difference is 2. Find the two numbers by writing and solving a system of equations.Calculations:Answer: _______________Let the 2 numbers be A and BA+B=30A-B=2Therefore by substitution2A=32A=16B=143. Two apples and three pears cost $3.45. Three apples and five pears cost $5.55. Find the cost of each type of fruit.Calculations:Answer: _______________A-ApplesP-pears2A+3P=3.453A+5P=5.55By substitution2A=1.2A=0.6P=0.751 apple=0.61 pear=0.754. Mary has a total of $5000 invested in two accounts. One account pays 5% and the other 8%. Her interest in the first Bear was $331. Write and solve a system of equations to find out how much she has invested in both accounts.Calculations:Answer: _______________Let 2 accounts be A and BA+B=50000.05A+0.08B=331By substitution0.6B=1620B=2700A=2300Therefore, amount invested in account A =$2,300Amount invested in account B=$ 2,7005. Terry is mailing two boxes. Together they weigh 21 lbs. If the smaller box is 5 lbs. less than the larger one, how much does each box weigh? Write and solve an equation that models this scenario.Calculations:Answer: _______________Let the 2 boxes be A and BA+B=21lbsA-B=5lbsBB substitution:2B=16B= 8lbsA= 13lbsTherefore,Bigger b ox B=13 lbsSmaller box A= 8lbs6. The length of a pool is 3 feet more than twice its width. If the perimeter of the pool is 72 feet, find the dimensions of the pool by writing and solving a system of equations.Calculations:Answer: _______________L=lengthW=widthL-2W=32L+2W=72By substitution6W=66W=11 feetsL=25 feetsTherefore,Length=25 feetsWidth=11 feets7. A desk and a chair cost $200 as a set. If the desk costs four times more than the chair, how much does each one cost. Write and solve using a system of equations.Calculations: