## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Section 7.2 - Systems of Linear Equations in Three Variables - Exercise Set - Page 829: 1

#### Answer

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

#### Work Step by Step

We have to check if the given point is a solution to the system, putting in the value $2$ for x, $-1$ for y and $3$ for z in all three equations: For the first equation: \begin{align} & 2-1+3=4 \\ & 1+3=4 \\ & 4=4 \end{align} This implies the point satisfies the first equation. For the second equation: \begin{align} & 2-2\left( -1 \right)-3=1 \\ & 2+2-3=1 \\ & 4-3=1 \\ & 1=1 \end{align} This implies the point satisfies the second equation. For the third equation: \begin{align} & 2\left( 2 \right)+1-2\left( 3 \right)=-1 \\ & 4+1-6=-1 \\ & 5-6=-1 \\ & -1=-1 \end{align} This implies the point satisfies the third equation. Thus, the ordered triple is a solution of the system.

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