Chapter 12.8, Problem 3MRE

To determine

To calculate: The solution set for the system of equations.

  $\begin{array}{c}2x-5y=3\\ -x+5y=6\end{array}$

Answer to Problem 3MRE

The solution set for the system of equations is $\left(9,3\right)$ .

Explanation of Solution

Given information:

The system of equations

  $\begin{array}{c}2x-5y=3\\ -x+5y=6\end{array}$

Calculation:

Consider the system of equations

  $\begin{array}{c}2x-5y=3\\ -x+5y=6\end{array}$

Use the method of elimination to solve the system above.

Add both the equations,

  $\begin{array}{ccccc}2x& -& 5y& =& 3\\ -x& +& 5y& =& 6\\ +\\ x& +& 0& =& 9\end{array}$

Therefore,

  $x=9$

Now substitute $x=9$ in the equation $-x+5y=6$ ,

  $\begin{array}{c}-x+5y=6\\ -9+5y=6\\ 5y=6+9\\ 5y=15\end{array}$

Simplified Further:

  $\begin{array}{c}5y=15\\ y=3\end{array}$

Therefore, solution is the coordinate pair, $\left(9,3\right)$ .

Thus, the solution set for the system of equations is $\left(9,3\right)$ .