Problem 43 - College Algebra

Question

How do you determine whether a given ordered triple is a solution of a system in three variables?

Step-by-Step Solution

Answer

To determine if an ordered triple is a solution to a system of three variables, substitute the values into the system of equations. If all equations hold true with these values, then the ordered triple is a valid solution to the system.

Step 1: Understand the given ordered triple

An ordered triple refers to a group of three numbers. These numbers correspond to the values of three variables, typically in the order \(x\), \(y\), \(z\). Given an ordered triple, identify the values that each variable should have.

Step 2: Substitute into the equations

For each equation in the system, replace \(x\), \(y\), \(z\) with the corresponding values from the ordered triple. After substituting the values, perform the calculations in the equation.

Step 3: Check if the equations hold true

Verify if the equations hold true after substituting the values from the ordered triple. If all equations in the system hold true after the substitution, then the given ordered triple is a solution to the system. If not, the ordered triple is not a solution of the system.