Skill Check over Substitution and Elimination after Homework

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Solve the given system by elimination: 2) -3x + 4y = -4 3x – 6y = 6

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Presentation transcript:

Skill Check over Substitution and Elimination after Homework Questions over hw? Skill Check over Substitution and Elimination after Homework

Questions over hw?

Skill Check

Solving Word Problems Using Systems

Summary of Methods 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. Elimination: Can be applied to any system, but it is especially convenient when a variable appears in different equations with coefficients that are opposites. Graphing: Can be easily written as y= for both.

What is the Best Method for the following? 1. y = 4x – 3 5x – 2y = 6 2. 4x – 5y = 13 2x + 5y = 5

What is the Best Method for the following? 5. 3x – 2y = 6 y = 2x – 4 6. x + y = 4 2x + 3y = 7

Steps Define all variables. What are you trying to find/solve? Write the system of equations. Solve using the best method & showing all steps. Check your solution. State your solution in sentence form.

1. You are selling tickets for a high school basketball game 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?

Solve Define variables: x = # of Student Tickets y = # of General Admin Tickets System of equations: x + y = 350 3x + 5y = 1450 y = 200 State your solution(s): x = 150 I sold 150 student tickets and 200 general adm. tickets.

2. At an Italian bistro, the cost 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 of a bowl of salad.

Solve Define variables: x = cost plate of spaghetti y = cost salad System of equations: 2x + y = 27.50 4x + 3y = 59.50 x = 11.50 State your solution(s): y = 4.50 A plate of spaghetti costs $11.50 and a salad costs $4.50.

3. Simon invests $1200 into two savings accounts 3. 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?

X = 350 Y = 850 X + Y = 1200 Solve Define variables: X = amount invested at 4% Y = amount invested at 5.9% System of equations: X + Y = 1200 0.04X + 0.059Y = 64.15 X = 350 State your solution(s): Simon invested $350 at 4% annual interest and invested $850 at 5.9% annual interest. Y = 850

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