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Addition/Subtraction discussed how to solve systems of two equations with two variables by the Addition/Subtraction method. Systems with three equations and three variables can also be solved using the Addition/Subtraction method.
Pick any two pairs of equations in the system. Then use addition and subtraction to eliminate the same variable from both pairs of equations. This leaves two equations with two variables--one equation from each pair. Solve this system using the Addition/Subtraction method. Then plug the solution back in to one of the original three equations to solve for the remaining variable.
Here, in step format, is how to solve a system with three equations and three variables:
Example: Solve the following system:
4x - 3y + z = - 10
2x + y + 3z = 0
- x + 2y - 5z = 17
4x - 3y + z = - 10 |
2x + y + 3z = 0 |
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
-5y - 5z = - 10
5y - 7z = 34
-12z = 24
Thus, z = - 2
-5y - 5(- 2) = - 10
-5y = - 20
Thus, y = 4
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