Chapter 6.5, Problem 26HP

To determine

To write a question to challenge the given conjecture

Explanation of Solution

Elimination is not always the best way to solve a system of equations.

In some cases, substitution or graphing methods are the best way to solve.

For example,

Consider the system of equations:

  $\begin{array}{l}33x+53y=7\\ 51x+13y=9\end{array}$

In such cases, elimination using addition, subtraction or multiplication won’t work properly. There is no variable with common coefficient in both the equations. In such cases, we can multiply coefficient either variables from the equation so that one of the variables gets eliminated. This makes a tedious process.

So, substitution or graphing methods may be helpful in these cases.