Question

How to solve set of 3 variable equations?

Answer 1

Here, in step format, is how to solve a system with three equations and three variables:

Pick any two pairs of equations from the system.

Eliminate the same variable from each pair using the Addition/Subtraction method.

Solve the system of the two new equations using the Addition/Subtraction method.

Substitute the solution back into one of the original equations and solve for the third variable.

Check by plugging the solution into one of the other three equations.


Example: Solve the following system:

4x - 3y + z = - 10
2x + y + 3z = 0
- x + 2y - 5z = 17

Pick two pairs:
4x - 3y + z = - 102x + y + 3z = 0and

Eliminate the same variable from each system:

4x - 3y + z = - 10
2x + y + 3z = 0

4x - 3y + z = - 10
-4x - 2y - 6z = 0

-5y - 5z = - 10

2x + y + 3z = 0
- x + 2y - 5z = 17

2x + y + 3z = 0
-2x + 4y - 10z = 34

5y - 7z = 34

Solve the system of the two new equations:

-5y - 5z = - 10
5y - 7z = 34

-12z = 24
Thus, z = - 2

-5y - 5(- 2) = - 10
-5y = - 20
Thus, y = 4

Substitute into one of the original equations:
- x + 2y - 5z = 17
- x + 2(4) - 5(- 2) = 17
- x + 18 = 17
- x = - 1
x = 1
Therefore, (x, y, z) = (1, 4, - 2).

Check: Does 2(1) + 4 + 3(- 2) = 0? Yes.


hope it helps








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