Question

Verify that the values of the variables listed are solutions of the system of equations. $$\begin{aligned} &\left\{\begin{aligned} 3 x+3 y+2 z=& 4 \\ x-y-z=& 0 \\ 2 y-3 z=&-8 \end{aligned}\right.\\ &x=1, y=-1, z=2\\ &(1,-1,2) \end{aligned}$$

Name: Problem 13, Chapter 11: Precalculus
Uploaded: 2020-07-03T19:11:10-08:00
Duration: 1 min 23 s
Channel: Kelly Hughes
Description: Verify that the values of the variables listed are solutions of the system of equations. { 3 x+3 y+2 z= 4 x-y-z= 0 2 y-3 z= -8 . x=1, y=-1, z=2 (1,-1,2)

   Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{aligned}
3 x+3 y+2 z=& 4 \\
x-y-z=& 0 \\
2 y-3 z=&-8
\end{aligned}\right.\\
&x=1, y=-1, z=2\\
&(1,-1,2)
\end{aligned}$$

Precalculus

Michael Sullivan 9th Edition

Chapter 11, Problem 13

Instant Answer

Solved by Expert Kelly Hughes

07/03/2020

Step 1

Step 1: First, we substitute the given values into the first equation: \[3(1)+3(-1)+2(2) = 3-3+4 = 4\] This is equal to the right side of the first equation, so the first equation is satisfied. Show more…

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Verify that the values of the variables listed are solutions of the system of equations. $$\begin{aligned} &\left\{\begin{aligned} 3 x+3 y+2 z=& 4 \\ x-y-z=& 0 \\ 2 y-3 z=&-8 \end{aligned}\right.\\ &x=1, y=-1, z=2\\ &(1,-1,2) \end{aligned}$$

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Key Concepts

Verification of a Solution

This process involves checking whether a set of proposed values satisfies each equation in the system. By substituting the values into each equation and confirming that all equalities hold true, one can prove that the candidate solution is valid.

System of Linear Equations

This concept involves a set of equations with multiple variables where each equation represents a line or plane in a coordinate system. The aim is to find a set of values that simultaneously satisfy all equations, which is fundamental in algebra and various applications in science and engineering.

Substitution Method

This is a technique where specific values are replaced for the variables in each equation of the system. It is used to transform and simplify the equations, making it easier to see if the substituted values result in true statements, thereby confirming the solution.

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