Chapter 12.8, Problem 2MRE

To determine

To calculate: The solution set for the system of equations with the help either substitution or elimination.

  $\begin{array}{l}x+y=10\\ x-2y=16\end{array}$

Answer to Problem 2MRE

The solution set for the system of equations is $\left(12,-2\right)$ .

Explanation of Solution

Given information:

The system of equations

  $\begin{array}{l}x+y=10\\ x-2y=16\end{array}$

Calculation:

Consider the system of equations

  $\begin{array}{l}x+y=10\\ x-2y=16\end{array}$

Use the method of substitution to solve the system above.

From the equation $x+y=10$ isolate the value of y ,

  $\begin{array}{c}x+y=10\\ y=10-x\end{array}$

Now substitute $y=10-x$ in the equation $x-2y=16$ ,

  $\begin{array}{c}x-2\left(10-x\right)=16\\ x-20+2x=16\\ 3x=16+20\\ 3x=36\end{array}$

Simplified further:

  $\begin{array}{l}3x=36\\ x=12\end{array}$

Now, substitute $x=12$ in the equation $y=10-x$ ,

  $\begin{array}{c}y=10-x\\ y=10-12\\ y=-2\end{array}$

Therefore, solution is the coordinate pair, $\left(12,-2\right)$ .

Thus, the solution set for the system of equations is $\left(12,-2\right)$ .