# Chapter 7 - Section 7.2 - Systems of Linear Equations in Three Variables - Exercise Set - Page 829: 4

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

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