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Problem 8

For the following exercises, determine whether the ordered triple given is the solution to the system of equations.

$$

\begin{aligned} 6 x-7 y+z &=2 \\-x-y+3 z &=4 \quad \text { and }(4,2,-6) \\ 2 x+y-z &=1 \end{aligned}

$$

Answer

the ordered triple $(4,2,-6)$ is not a solution to the system.

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## Discussion

## Video Transcript

All right, Uh, is four to negative six A solution? Thio following system. They're so yeah, it's a solution to the system. Then this X This Why in this Z are gonna make all three equations true? If any of the equations is false, when it substitute these values in, then we'll be done with that problem because we'll know that it's not a solution. Tested it in all. So, um, let's start doing our substitution. So 1st 16 times for minus seven times two plus negative six. We wanted out of this daddy too. All right, so this is 24 minus 14 which is 10 and then 10 plus negative. Six is actually four. This is not able to. All right. Well, in that case, this is not a solution.

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