Chapter 12.8, Problem 4MRE

To determine

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

  $\begin{array}{c}5x+3y=5\\ -4x+3y=10\end{array}$

Answer to Problem 4MRE

The solution set for the system of equations is $\left(5,10\right)$ .

Explanation of Solution

Given information:

The system of equations

  $\begin{array}{c}5x+3y=5\\ -4x+3y=10\end{array}$

Calculation:

Consider the system of equations

  $\begin{array}{c}5x+3y=5\\ -4x+3y=10\end{array}$

Use the method of elimination to solve the system above.

Multiply the equation $4x+3y=10$ by $-1$ .

  $-4x-3y=-10$

Add both the equations,

  $\begin{array}{ccccc}5x& +& 3y& =& 5\\ -4x& -& 3y& =& -10\\ \\ x& +& 0& =& -5\end{array}$

Therefore,

  $x=-5$

Now substitute $x=-5$ in the equation $5x+3y=5$ ,

  $\begin{array}{c}5x+3y=5\\ 5\cdot -5+3y=5\\ -25+3y=5\\ 3y=5+25\end{array}$

Simplified Further:

  $\begin{array}{c}3y=5+25\\ 3y=30\\ y=10\end{array}$

Therefore, solution is the coordinate pair, $\left(5,10\right)$ .

Thus, the solution set for the system of equations is $\left(5,10\right)$ .