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Applications of Systmes

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Jessica Polk
Jessica Polk

The document provides instructions and examples for solving systems of linear equations in five steps: 1) define variables, 2) write the system of equations, 3) solve using substitution, elimination, or graphing, 4) state the solution, 5) check the solution. It then shows four examples of word problems solved using this process, finding the number of student and general admission tickets sold, amounts invested at different interest rates, costs of food items, and time spent walking and jogging.

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1)Substitution: Requires that one of the variables be isolated on one side of the equation. It is especially convenient when one of the variables has a coefficient of 1 or -1. 2)Elimination: Can be applied to any system, but it is especially convenient when a variable appears in different equations with coefficients that are opposites. 3)Graphing: Can provide a useful method for estimating a solution.
1. Define all variables. 2. Write the system of equations. 3. Solve using the best method & showing all steps. 4. State your solution in sentence form. 5. Check your solution.
1. You are selling tickets for a high school basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450. How many of each type of ticket did you sell?
Define variables: System of equations: State your solution(s): Solve S = # of Student Tickets G = # of General Admin Tickets S + G = 350 3S + 5G = 1450 G = 200 S = 150I sold 200 general admission tickets and 150 student tickets.
2. Simon invests $1200 into two savings accounts. One account earns 4% annual interest and the other earns 5.9% annual interest. At the end of 1 year, Simon earned $64.15 in interest. How much did he invest at each rate?
Define variables: System of equations: State your solution(s): Solve X = amount invested at 4% Y = amount invested at 5.9% X + Y = 1200 0.04X + 0.059Y = 64.15 X = 350 Y = 850Simon invested $350 at 4% annual interest and invested $850 at 5.9% annual interest.
3. At an Italian bistro, the costs of 2 plates of spaghetti and 1 salad is $27.50. The cost for 4 plates of spaghetti and 3 salads is $59.50. Find the cost of a plate of spaghetti and a salad.
Define variables: System of equations: State your solution(s): Solve P = cost plate of spaghetti S = cost salad 2P + S = 27.50 4P + 3S = 59.50 P = 11.50 S = 4.50A plate of spaghetti costs $11.50 and a salad costs $4.50.
4. Peggy walks at a rate of 2 miles per hour and jogs at a rate of 4 miles per hour. She walked and jogged 3.4 miles in 1.2 hours. For how long did Peggy jog and for how long did she walk?
Define variables: System of equations: State your solution(s): Solve W = hours walked J = hours jogged W + J = 1.2 2W + 4J = 3.4 W = .7 J = .5Peggy walked for 0.7 hours and jogged for 0.5 hours.

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Applications of Systmes

  • 1. 1)Substitution: Requires that one of the variables be isolated on one side of the equation. It is especially convenient when one of the variables has a coefficient of 1 or -1. 2)Elimination: Can be applied to any system, but it is especially convenient when a variable appears in different equations with coefficients that are opposites. 3)Graphing: Can provide a useful method for estimating a solution.
  • 2.
  • 3. 1. Define all variables. 2. Write the system of equations. 3. Solve using the best method & showing all steps. 4. State your solution in sentence form. 5. Check your solution.
  • 4. 1. You are selling tickets for a high school basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450. How many of each type of ticket did you sell?
  • 5. Define variables: System of equations: State your solution(s): Solve S = # of Student Tickets G = # of General Admin Tickets S + G = 350 3S + 5G = 1450 G = 200 S = 150I sold 200 general admission tickets and 150 student tickets.
  • 6. 2. Simon invests $1200 into two savings accounts. One account earns 4% annual interest and the other earns 5.9% annual interest. At the end of 1 year, Simon earned $64.15 in interest. How much did he invest at each rate?
  • 7. Define variables: System of equations: State your solution(s): Solve X = amount invested at 4% Y = amount invested at 5.9% X + Y = 1200 0.04X + 0.059Y = 64.15 X = 350 Y = 850Simon invested $350 at 4% annual interest and invested $850 at 5.9% annual interest.
  • 8. 3. At an Italian bistro, the costs of 2 plates of spaghetti and 1 salad is $27.50. The cost for 4 plates of spaghetti and 3 salads is $59.50. Find the cost of a plate of spaghetti and a salad.
  • 9. Define variables: System of equations: State your solution(s): Solve P = cost plate of spaghetti S = cost salad 2P + S = 27.50 4P + 3S = 59.50 P = 11.50 S = 4.50A plate of spaghetti costs $11.50 and a salad costs $4.50.
  • 10. 4. Peggy walks at a rate of 2 miles per hour and jogs at a rate of 4 miles per hour. She walked and jogged 3.4 miles in 1.2 hours. For how long did Peggy jog and for how long did she walk?
  • 11. Define variables: System of equations: State your solution(s): Solve W = hours walked J = hours jogged W + J = 1.2 2W + 4J = 3.4 W = .7 J = .5Peggy walked for 0.7 hours and jogged for 0.5 hours.