Chapter 12.8, Problem 5MRE

To determine

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

  $\begin{array}{l}x-y=0\\ x+y=4\end{array}$

Answer to Problem 5MRE

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

Explanation of Solution

Given information:

The system of equations

  $\begin{array}{l}x-y=0\\ x+y=4\end{array}$

Calculation:

Consider the system of equations

  $\begin{array}{l}x-y=0\\ x+y=4\end{array}$

Use the method of substitution to solve the system above.

From the equation $x+y=4$ isolate the value of y ,

  $\begin{array}{c}x+y=4\\ y=4-x\end{array}$

Now substitute $y=4-x$ in the equation $x-y=0$ ,

  $\begin{array}{c}x-y=0\\ x-4+x=0\\ 2x=4\\ x=2\end{array}$

Now, substitute $x=2$ in the equation $y=4-x$ ,

  $\begin{array}{c}y=4-x\\ y=4-2\\ y=2\end{array}$

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

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