2. Critique the Solution to This System. If It Is Incorrect, Find the Correct Answer

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5.04 Linear Systems

1. Solve this system.

Answer: (,)

2. Critique the solution to this system. If it is incorrect, find the correct answer.

Proposed Answer:

Add the equations together using the addition method to get:

Solve for y:

Plug the solution for y back into one of the original equations and solve for x:

Critique:

3. Critique the solution to this system. If it is incorrect, find the correct answer.

Proposed Answer:

Multiply the second equation by -3 and then add the equations together using the addition method.

Solve for y:

y = 1/3

Plug the solution for y back into one of the original equations and solve for x:

6(1/3) – 3y = 1

2 – 3y = 1

-3y = -1

y = 1/3

Critique:

4. Solve the system.

Answer: (,)

5. Solve the system.

Answer: (,,)

6. Solve the system.

Answer: x = , y = , z =

7. Create a system of equations and solve the problem.

You have 37 coins that are nickels, dimes, and pennies. The total value of the coins is $1.55. There are twice as many pennies as dimes. Find the number of each type of coin in the bank.

Answer: Let n be the number of nickels, d be the number of dimes, and p be the number of pennies. The system is

Enter Equation 1 here

Enter Equation 2 here

Enter Equation 3 here

The solution is pennies, dimes and nickels.

8. Create a system of equations and solve the problem.

You have 36 coins that are nickels, dimes, and quarters. The total value of the coins is $5.00. The number of quarters is 1 more than the number of dimes, and the number of dimes is 1 more than the number of nickels. Find the number of each type of coin in the bank.

Answer: Let n be the number of nickels, d be the number of dimes, and q be the number of quarters. The system is

Enter Equation 1 here

Enter Equation 2 here

Enter Equation 3 here

The solution is quarters, dimes and nickels.

9. Johnny invested $20,000. A portion returned 5% and another portion returned 8%. The total interest earned on the investment was $1150. Write a system of equations for this situation and determine how much of the original investment was invested at the 5% rate and how much was invested at the 8% rate.

Answer: Let x be the amount invested that earned 5% and y be the amount invested that earned 8%. System of equations:

Enter Equation 1 here

Enter Equation 2 here

Solution: x = $, y = $.

10.A concert is being held in your hometown. 1500 tickets are sold. Adult tickets are $10.50and child’s tickets are $7.50. If a total of $13950 worth of tickets were sold, determine how many adult tickets and how many child tickets were sold.

Answer: Let x be the number of adult tickets and y be the number of child tickets. System of equations:

Enter Equation 1 here

Enter Equation 2 here

Solution: x = and y =