## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Section 7.2 - Systems of Linear Equations in Three Variables - Exercise Set - Page 829: 3

#### Answer

Yes, the ordered triple is a solution of the system.

#### Work Step by Step

We have to check if the provided point is a solution to the system, putting in the value $4$ for x, $1$ for y and $2$ for z in all three equations. For the first equation: \begin{align} & 4-2\left( 1 \right)=2 \\ & 4-2=2 \\ & 2=2 \end{align} This implies the point satisfies the first equation. For the second equation: \begin{align} & 2\left( 4 \right)+3\left( 1 \right)=11 \\ & 8+3=11 \\ & 11=11 \end{align} This implies the point satisfies the second equation. For the third equation: \begin{align} & 1-4\left( 2 \right)=-7 \\ & 1-8=-7 \\ & -7=-7 \end{align} This implies the point satisfies the third equation. Thus, the ordered triple is a solution of the system.

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