Verifying Ordered Triples in Equations

The video tutorial explains how to determine if an ordered triple is a solution to a system of three equations. It involves plugging the values of x, y, and z from the triples into the equations and checking if they satisfy all the equations. The process is demonstrated with examples, showing how to eliminate incorrect triples and verify the correct one. A second example is provided with a different set of equations, illustrating the method of checking each triple against the equations to find the correct solution.

What is the main task when dealing with ordered triples in systems of equations?

• To solve for a single variable

• To determine if the triple is a solution

• To find the sum of the triples

• To rearrange the equations

What is the first step in verifying if an ordered triple is a solution?

• Rearrange the equations

• Plug the triple into the equations

• Graph the equations

• Solve the equations

What happens if an ordered triple does not satisfy one of the equations?

• It is still a possible solution

• It is eliminated as a possible solution

• It needs to be rearranged

• It should be graphed

In the first example, what was the result of checking the first equation with triple A?

• It satisfied the equation

• It did not satisfy the equation

• It was inconclusive

• It needed rearrangement

Why was ordered triple A eliminated?

• It satisfied all equations

• It was not checked

• It did not satisfy the second equation

• It was not a valid triple

What was the outcome of checking ordered triple B?

• It satisfied all equations

• It was the correct solution

• It did not satisfy the first equation

• It did not satisfy the equations

What was the result of checking the first equation with triple C?

• It satisfied the equation

• It did not satisfy the equation

• It was inconclusive

• It needed rearrangement

What confirmed that ordered triple C was the correct solution?

• It satisfied the first equation only

• It satisfied all three equations

• It was the only option left

• It was guessed correctly

What is the first equation in the new problem introduced?

• x - y + z = 4

• x + y + z = 4

• x - y - z = 4

• x + y - z = 4

Why was option A eliminated immediately in the new problem?

• It was guessed incorrectly

• The numbers did not add up to 4

• It was not checked

• It was not a valid triple