Chapter 9.9, Problem 5OE

To determine

To calculate: To find two ordered triples that satisfy the equation

Answer to Problem 5OE

  $\left(1,2,4\right)$ and $\left(2,1,4\right)$ solution of equation

Explanation of Solution

Given information: Equation is $x+y+z=7$

Calculation:

Given the equation as follows:

  $x+y+z=7$

Consider ordered triples $\left(1,2,4\right)$ and $\left(2,1,4\right)$

Check if $\left(1,2,4\right)$ is the solution:

Substituting the values in LHS of equation:

  $\begin{array}{l}LHS:1+2+4\\ LHS:7\end{array}$

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

Thus, $\left(1,2,4\right)$ is solution of the equation

Check if $\left(2,1,4\right)$ is the solution:

Substituting the values in LHS of equation:

  $\begin{array}{l}LHS:2+1+4\\ LHS:7\end{array}$

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

Thus, $\left(2,1,4\right)$ is solution of the equation

Conclusion:

Hence, $\left(1,2,4\right)$ and $\left(2,1,4\right)$ solution of equation