Problem 43

Question

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

Step-by-Step Solution

Verified
Answer
To determine whether a given ordered triple is a solution of a system in three variables, replace x, y, and z in each equation of the system with values from the ordered triple. If all equations hold true after substituting these values, the ordered triple is a solution to the system.
1Step 1: Identify the Ordered Triple and the System of Equations
The ordered triple typically has the form (x, y, z). Your system of equations will be composed of multiple equations, all containing the variables x, y, and z.
2Step 2: Substitute the Ordered Triple into the System of Equations
Replace the variables x, y, and z in each equation of the system by the values from your ordered triple.
3Step 3: Verify if Equations are True
After substituting the values from the ordered triple, check if the new expression acquired for each equation holds true. If all equations hold true, then the given ordered triple is a solution to the system.