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In Problems 9-18, verify that the values of the variables listed are solutions of the system of equations. $\left\{\begin{aligned} 4 x-5 z & =6 \\ 5 y-z & =-17 \\ -x-6 y+5 z & =24\end{aligned}\right.$ $x=4, y=-3, z=2 ;(4,-3,2)$ 

   In Problems 9-18, verify that the values of the variables listed are solutions of the system of equations.
 $\left\{\begin{aligned} 4 x-5 z & =6 \\ 5 y-z & =-17 \\ -x-6 y+5 z & =24\end{aligned}\right.$
$x=4, y=-3, z=2 ;(4,-3,2)$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Michael Sullivan 4th Edition
Chapter 10, Problem 18 ↓

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\] Plugging in the values: \[ 4(4) - 5(2) = 16 - 10 = 6. \] Since the left-hand side equals the right-hand side (6 = 6), the values satisfy the first equation.  Show more…

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In Problems 9-18, verify that the values of the variables listed are solutions of the system of equations. $\left\{\begin{aligned} 4 x-5 z & =6 \\ 5 y-z & =-17 \\ -x-6 y+5 z & =24\end{aligned}\right.$ $x=4, y=-3, z=2 ;(4,-3,2)$
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Key Concepts

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Substitution Method
This method involves replacing the variables in the equations with the provided values in order to simplify and verify the equations. It is a straightforward technique to check the validity of a solution in linear systems.
Systems of Linear Equations
This concept involves a collection of linear equations with several variables that are solved simultaneously. Understanding this is essential because it provides a framework for determining whether a set of variable values satisfies all the given equations at once.
Verification of a Proposed Solution
This concept refers to the process of confirming that a given set of values actually satisfies all the equations in the system. It involves substituting the values into each equation and checking if the resulting statements are true.
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In Problems $9-18$, verify that the values of the variables listed are solutions of the system of equations. $$ \begin{array}{l} \left\{\begin{array}{l} 2 x-y=5 \\ 5 x+2 y=8 \end{array}\right. \\ x=2, y=-1 ;(2,-1) \end{array} $$
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