Chapter 9.9, Problem 4OE

To determine

To calculate: To find which of the ordered triples is a solution of the equation

Answer to Problem 4OE

  $\left(-2,0,2\right)$ is solution of equation

Explanation of Solution

Given information: Equation is $x-3y+4z=6$

Calculation:

Given the equation as follows:

  $x-3y+4z=6$

Check if $\left(-2,0,2\right)$ is the solution:

Substituting the values in LHS of equation:

  $\begin{array}{l}LHS:-2-3\left(0\right)+4\left(2\right)\\ LHS:-2-0+8\\ LHS:6\end{array}$

Left hand side of equation is equal to right hand side of equation.

Thus, $\left(-2,0,2\right)$ is solution of the equation

Check if $\left(2,-2,0\right)$ is the solution:

Substituting the values in LHS of equation:

  $\begin{array}{l}LHS:2-3\left(-2\right)+4\left(0\right)\\ LHS:2+6+0\\ LHS:8\end{array}$

Left hand side of equation is NOT equal to right hand side of equation.

Thus,

  $\left(2,-2,0\right)$ is NOT solution of the equation

Conclusion:

Hence, $\left(-2,0,2\right)$ is solution of equation