Chapter 6.3, Problem 38PPE

To determine

Which is best substitution method or elimination method.

Answer to Problem 38PPE

Elimination method is best.

Explanation of Solution

Given data:

  $\begin{array}{l}15x+120y=45\\ 5x+60y=15\end{array}$

In substitution method we have to substitute one variable in the other equation but sometimes it changes the degree of equation which become more complicated for solving whereas in elimination method one variable had been cancel so it is more easier to solve.

For example;

  $\begin{array}{l}15x+120y=45\\ 5x+60y=15\end{array}$

Firstly by substitution:

  $\begin{array}{l}15x+120y=45\\ 5x+60y=15\\ y=\frac{15-5x}{60}\\ putting\text{ in 1}\\ \text{15x}+\text{120(}\frac{15-5x}{60}\text{)}=\text{45}\end{array}$

Now by Elimination method:

  $\begin{array}{l}15x+120y=45\\ \frac{3(5x+60y=15)}{}\\ 15x+120y=45\\ \frac{(15x+180y=45)}{}\\ 120y-180y=0\\ y=0\\ x=3\end{array}$

The elimination method has substitution in it as a part of the solution. As we solve substitution method the variable which was canceled been replaced by the other variable so in elimination method substitution also included.

Conclusion:

Elimination method is best.