Systems Of Linear Equations Lesson #5: Number and Money Applications We have discussed three different methods for solving systems of equations. Methods for Solving Systems of Equations Graphing Substitution Elimination In this lesson we apply these methods in problem solving. Problem Solving We can solve a variety of types of problems using a system of equations. There are four general steps to problem solving which are shown in the flowchart below. Step 1 Introduce variables to represent the unknown values. Step 2 Form a system of equations involving the variables. Step 3 Solve the system. Step 4 Answer the problem and check the solution. Number Applications The difference between two numbers is 9. The larger number is 3 more than twice the smaller number. Find the numbers. Let x be the larger number and y be the smaller number x-y=9 "the difference between two numbers is 9" x=2y+3 "larger number is 3 more than twice the smaller number" x-y=9 (2y+3)-y=9 y=6 x=2y+3 x=2(6)+3 x=15 CHECK: x-y=9 LS: 15-6=9 RS=9 LS=RS x=2y+3 LS: 15 RS: 2(6)+3=15 LS=RS The numbers are 15 and 6 Class Ex. #2 The perimeter of a rectangle is 40 metres. The width is 4 metres less than the length. Find the dimensions of the rectangle. [rectangle image] 2x + 2y = 40 y = x - 4 2x + 2y = 40 2x + 2(x-4) = 40 2x + 2x - 8 = 40 4x = 48 x = 12 sub into formula found. y=x-4 sub into equation to solve "y" y = x - 4 y = (12) - 4 y = 8 check 2x + 2y = 40 LS : 2(12) + 2(8) = 40 RS: 40 y = x - 4 LS: 8 RS: 12-4 = 8 The length is 12m The width is 8m Money Applications Class Ex. #3 Gary had a total of $260 in five-dollar bills and ten-dollar bills. If he has 33 bills in total, how many of each denomination does he have? Let x be the number of five-dollar bills and y be the number of ten-dollar bills. 5x + 10y = 260 x + y = 33 (x 5) 5x + 10y = 260 -5x + 5y = 165 (Subtract) 5y = 95 y = 19 sub into equation to solve for x x + y = 33 x + (19) = 33 x = 14 check answers 5x + 10y = 260 LS: 5(14) + 10(19) = 260 RS: 260 LS = RS x + y = 33 LS: (14) + (19) = 33 RS: 33 LS = RS There are 14 five-dollar bills and 19 ten-dollar bills Complete Assignment questions #1 - #10

Number and Money Applications

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