Chapter 9.9, Problem 1OE

To determine

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

Answer to Problem 1OE

  $\left(3,0,-4\right)$ is solution of the equation.

Explanation of Solution

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

Calculation:

Given the equation as follows:

  $x+y-z=7$

Check if $\left(4,-2,5\right)$ is the solution:

Substituting the values in LHS of equation:

  $\begin{array}{l}LHS:4+\left(-2\right)-5\\ LHS:4-2-5\\ LHS:-3\end{array}$

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

Thus, $\left(4,-2,5\right)$ is not solution of the equation.

Check if $\left(3,0,-4\right)$ is the solution:

Substituting the values in LHS of equation:

  $\begin{array}{l}LHS:3+0-\left(-4\right)\\ LHS:3+4\\ LHS:7\end{array}$

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

Thus, $\left(3,0,-4\right)$ is solution of the equation.

Conclusion:

Hence, $\left(3,0,-4\right)$ is solution of the equation.