Chapter 6.3, Problem 39HP

To determine

To describe the most beneficial time to use elimination to solve the system of equations.

Explanation of Solution

The most beneficial time to use the elimination method is when the coefficients of the variables are same with similar or opposite in sign or if the coefficients are multiples of one another.

For example,

Consider the system of equations

  $\begin{array}{c}x+y=5\\ -x+2y=10\end{array}$

Adding both the equations will give us the solution for y eliminating x

  $\begin{array}{c}\Rightarrow (x+y)(-x+2y)=10+5\\ \Rightarrow 3y=15\\ \Rightarrow y=5\end{array}$

Substituting the value of y in (1)

  $\begin{array}{l}\Rightarrow x+y=5\\ \Rightarrow x=5-5\\ \Rightarrow x=0\end{array}$