Chapter 6.3, Problem 13P

Open-Ended Write a system for which using the elimination method to solve the system is easier than the substitution method. Explain.

To determine

To state:Using the elimination method to solve the system.

Answer to Problem 13P

The system is:

  $\begin{array}{l}3x-2y=5\\ -3x+7y=2\end{array}$

Explanation of Solution

The elimination method is simpler than the replacement solution for statistical systems. The termination method is so called because the actual system is replaced (if necessary) by an equal system, where the addition of these two numbers removes one variable.

Example: - (a system ideally suited to the elimination method.)

  $\begin{array}{l}3x-2y=5\\ -3x+7y=2\end{array}$

According to question,

  $\begin{array}{l}3x-2y=5\\ -3x+7y=2\\ add:5y=7\end{array}$

Since, Notice that there is a3x in the first equation and a-3x in the second equation. Adding the two equations elimination the variable x.

  $y=\frac{7}{5}$ (Solve for y.)

  $\begin{array}{l}3x-2\left(\frac{7}{5}\right)=5\\ 3x=5+\frac{14}{5}\\ 3x=\frac{39}{5}\\ x=\frac{39}{5\times 3}\\ x=\frac{39}{15}\end{array}$

(Since, substitute this value of y back into either original equation (preferably, a simple one) and solve for x.)

  $x=\frac{15}{3}$ (Report all number as fractions in simplest form)

The unique solution is the order pair $\left(\frac{15}{5},\frac{7}{5}\right).$