Chapter 6.3, Problem 36HP

To determine

To formulate a general rule for creating a system of equations using addition to eliminate one variable

Explanation of Solution

In case of elimination, one of the two variables can be eliminated by either adding the given system of equations or by subtracting them.

Addition of the system of equations is possible, if the coefficient of one of the variables is the negative of the other variable.

For Example:

Consider the equation $2x+3y=13.$

The coefficient of the above equation is 2.

Addition in elimination method is possible if the other equation has an x coefficient to be -2.

Let the other equation be $-2x+y=3.$

So, when these two equations are added, the variable x is eliminated.

  $\begin{array}{l}\Rightarrow (2x+3y)+(-2x+y)=13+3\\ \Rightarrow 4y=16\end{array}$

So, the general rule for creating a system of equations using addition to eliminate one variable is that “The coefficient of one of the variables in an equation has to be its additive inverse (negative) in the other equation”