In Problems 9-18, verify that the values of the variables...

In Problems 9-18, verify that the values of the variables listed are solutions of the system of equations.
$\left\{\begin{aligned} 3 x+3 y+2 z & =4 \\ x-3 y+z & =10 \\ 5 x-2 y-3 z & =8\end{aligned}\right.$ $x=2, y=-2, z=2 ;(2,-2,2)$

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Key Concepts

Substitution Method

The substitution method involves replacing the variables in an equation with specific numerical values to evaluate whether the equation is satisfied. This is a common technique used in solving and verifying solutions to systems of equations, as it directly demonstrates whether the given numbers fulfill the required conditions of the system.

Solution Verification

Solution verification is the process of checking whether a proposed set of values satisfies all equations in a system. This involves substituting the values into each equation and confirming the resulting expressions hold true. This step is essential to ensure the accuracy and validity of the solution.

System of Equations

A system of equations is a set of two or more equations with a common set of unknowns. The goal is to find values for the variables that satisfy all the equations simultaneously. This concept is foundational in algebra and is used to model problems with multiple conditions or constraints.

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