# Honors Algebra 2: Systems of 3 Linear Equations

• Class: Honors Algebra 2
• Author: Peter Atlas
• Text: Algebra and Trigonometry: Structure and Method, Brown

Calculator: You may use a calculator for help with the arithmetic, but you may not use a systems program or matrices.

Solve the following systems.

1. $$2x + 3y + 6z = 13 \\ 3x + 4y + 2z = 11 \\ x - 3y + 5z = -5$$
2. Solution (-1, 3, 1)
3. $$2x + y - z = -1 \\ -3x + 2y + 2z = 9 \\ x + y - z = 0$$
4. Solution (-1, 2, 1)
5. $$6x + 3y + 2z = 2 \\ -7x -5y + 3z = 22 \\ x + 2y - 5 z= -24$$
6. Solution (0, -2, 4)
7. $$3x + 5y - 7z = -1 \\ -2x + 7y - 3z = -2 \\ x - y + z = -1$$
8. Solution (-1, -1, -1)
9. $$5x + 3y - 2z = 0 \\ 9x + 3y + 10z = 0 \\ 7x - 9y + 3z = 0$$
10. Solution This is a homogeneous system with the single solution (0, 0, 0)
11. $$-2x + 4z = 9y + 38 \\ z = 2x - 3y -19 \\ 5x + 3y - 4z -1 = 0$$
12. Solution (5, -4, 3)
13. $$3x - 9y + 7z = -21 \\ -4x + 5y - 2z = 5 \\ -11x + y + 12z = -53$$
14. Solution (-2, -3, -6)
15. $$-2x - 8y - 7z = 87 \\ x + 9y - 6z = -2 \\ -10x + 4y - 5z = 5$$
16. Solution (1, -5, -7)
17. $$-11x + 3y + 12z = 61 \\ -12x - 11y + 8z = 195 \\ -10x - 6y - 2z = 134$$
18. Solution (-8, -9, 0)
19. $$3x + 4y + 9z = -51 \\ -y - 5z = 24 \\ -11x - 7y - 12z = 55$$
20. Solution (4, -9, -3)
21. $$10x + 3y - z = -55 \\ 3x - 6y - 6z = 36 \\ -6x + 2y - 9z = 106$$
22. Solution (-6, -1, -8)
23. $$4y + 11z = 85 \\ -3x + 6y - 3z = 3 \\ -8x - 9y - 12z = -70$$
24. Solution (-4, 2, 7)
25. $$4x + y - 2z = 0 \\ 2x - 3y + 3z = 9 \\ -6x - 2y + z = 0$$
26. Solution $$\displaystyle \left( \frac{3}{4}, -2, \frac{1}{2} \right)$$
27. $$x - y = 2 \\ 3x + z = 11 \\ y - 2z = -3$$
28. Solution (3, 1, 2)
29. In a coin bank, there are three times as many dimes as there are nickles and quarters combined. The total value of the 24 coins (all dimes, nickles, and quarters) is \$2.90. How many of each kind of coin are there?
30. Solution 18 dimes, 4 quarters, 2 nickles