Exercise 5 Page 171

Both the Substitution Method and the Elimination Method are useful to solve systems of equations. In this exercise, we will review how the Substitution Method works, and then we will decide when it is convenient to use it.

How Does the Substitution Method Work?

In a system of three equations, this method starts by reducing the system to one of two variables. To do this, we isolate one of the variables from one the system equations, then we substitute it in the remaining equations to eliminate said variable.

At this point we can continue by solving the new system to find the values for the variables $x$ and $y$ in this case. Once they are found, we can substitute their values in any of the equations of the original system to find the missing variable.

When Is It Preferred?

As the Substitution Method works by isolating a variable in one of the equations and then substituting it in the others, having a system in which we can solve for one variable easily or having it already isolated can facilitate using this method. However, preferences may vary, and we are always free to choose the method we like.