Mixed Review of Systems Name ______

Solve each system using the given method. Show your answer(s) as ordered pairs.

Substitution

1. 4x – 2y = 13 6. = 0

y = x – 4 = 3

7. x2 + y2 = 10

2. 2x + 5y = 32 x2 – y2 = 8 3y = x + 17

2 3. y = 2x 8. 2x – 6y = 14

2 2x + 3y = 32 3x – 9y = 21

Use any algebraic method.

9. 5x + y – z = 6 4. y = x – 7 x + y + z = 12 y = x + 4 2x + y = 7

10. x + 4y – 2z = 12 Elimination 3x – y + 4z = 6 5. 2x – 3y = -8 -x + 3y + z = -9 4x = 14 – 4y

11. x + y + z = 3 4x + 4y + 4z = 7 quarters. The face value of the collection is $80.00. You have fifty more nickels 3x – y + 2z = 5 than dimes. How many of each coin do you have?

12. x + y + z = 4

x + y – z = 4 14. A diluted saline solution is needed for 3x + 3y + z = 12 routine procedures in a hospital. The supply room has a large quantity of 20% solution and 40% solution. How much of each should they use to make 10 liters of a 25% solution? Write and solve a system to answer each question.

15. Write an equation for the parabola that passes through (1,4), (-1,-6), and (-2,-5). 13. You have a collection of 500 rare coins consisting of nickels, dimes, and

Use an augmented matrix and elementary row operations to solve each system.

16. x + 2y = 5

2x + y = -2

17. 3x – 4y = 1

5x + 2y = 19 18. x – y + 5z = -6

3x + 3y – z = 10

x + 3y + 2z = 5

19. y = x – 1

y = 6 + z

z = -1 – x

20. 2x + 3y + z = 9

4x – y + 3z = -1

6x + 2y – 4z = -8