Chapter 5.3, Problem 29E

To determine

To find: Which method has fewer steps to solve elimination or substitution?

Answer to Problem 29E

The steps of the calculation depend on the type of linear system, both elimination and substitution can be easy and hard.

Explanation of Solution

Given information: Which method has fewer steps to solve elimination or substitution?

We take two following examples to check friend’s statement.

  $\{\begin{array}{l}y=2x+1\\ x-5y=-5\end{array}$

The above-written equations can be solved by the substitution method easily because there is an isolated variable is present.

However, for the elimination method, it will become too hard to solve because there are no common factors between both equations.

Take the second example,

  $\{\begin{array}{l}5x+2y=20\\ 5x-2y=-2\end{array}$

The above-written equations can be hard to solve by substitution method because it takes tedious calculation to change the one variable to another variable.

However, for the elimination method, it will become easy to solve because there are common factors between both equations.

Hence, the calculation and the steps of calculation depend upon the linear system, both elimination and substitution can be easy and hard.