# 1.6 Solving Systems of Linear Equations in Three Variables

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```					010212                                                                     Name ______________________________
PMa. 11                                                                    Block ______

1.6 Solving Systems of Linear Equations
in Three Variables Worksheet
1. Is (2, -1, 5) a solution of this system of equations?

3x - 2y - z = 3
x + 5y + 2z = 7
4x + 11y + 7z = 32

__________________________________________

Solve each system of equations.

2. a + b - 2c = 9
2a - b - 3c = 13
3a + 2b - 4c = 22

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010212                                                                      1.6 Solving Systems of Linear Equations
PMa. 11                                                                          in Three Variables Worksheet

3. 2x + y - 5z = 23
4x - 3y + z = 23
x - 2y - 3z = 18

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4. 5p - 9q + r = -8
p + 4q - r = 1
3p + q - 3r = 14

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5. 4x + 3y + 5z = 39
5x - 2y - 3z = 29
7x + 4y - 2z = 29

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-2-
010212                                                                     1.6 Solving Systems of Linear Equations
PMa. 11                                                                         in Three Variables Worksheet

6. x - 3y + 4z = 19
2x - 5y = 24
y + 3z = -3

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7.
x y z
   11
2 5 2
2x 2y z
    2
3    5 3
3x 3y
    z  18
4     2

................................................................................

-3-
010212                                                                     1.6 Solving Systems of Linear Equations
PMa. 11                                                                         in Three Variables Worksheet

8. The sum of three integers is 54. The first integer is twice the difference between the
second and third integers. The second is 38 more than twice the third. Find the integers.

................................................................................
9. Solve the system of equations and interpret the solution.

4x + 3y - 2z = 6
3x + 4y - 3z = 7
x - 8y + 7x = -11

................................................................................

-4-

```
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