Chapter 2.1, Problem 1CFU

To determine

To write: a system of equation which is easier to solve by substitution method rather than elimination method and give explanation.

Answer to Problem 1CFU

An example of system of equations that is easier to solve by substitution rather than elimination is shown below.

  $\begin{array}{c}x=y\\ y-2=0\end{array}$

Explanation of Solution

Given information:

Step to solve system of three equation system.

Method used: Substitution rather than elimination method

Calculation:

Let’s look at system of equation given below.

  $\begin{array}{l}x=y\\ y-2=0\end{array}$

In this kind of equations, it is easier to substitute the value of x in the other equation solve for y. Such expression is easier to solve by substitution method.

Let’s represent an expression with A-Z denoting the constants and a-z denoting the unknown variables. Now, identify which expression is easier to solve by elimination method.

  $\begin{array}{c}\text{ A}a+\text{B}b+\text{C}c\mathrm{....}+\text{Z}z=\text{Constant}\\ -\left(\text{A}a+\text{B}b+\text{C}c\mathrm{....}+\text{Y}y\right)+\text{Z}z=\text{Constant}\end{array}$

If the system of equation with expression $\left(\text{A}+\text{B}+\text{C}\mathrm{....}+\text{Y}\right)$ is positive in one equation and negative in other, where one expression Z remains with unknown; then it is easier to eliminate all but one expression. Sometimes the expression can be made negative by multiplying it with $-1$ . Thus, the critical factor is $\left(\text{A}+\text{B}+\text{C}\mathrm{....}+\text{Y}\right)$ .