Introduction to Equations


Let's glance at an example:


A defense officer wants to know how many parachutes they have. He asked his subordinate for this number and he was told that number of parachutes is a function of the number of soldiers; i.e., the number of parachutes is twice the number of soldiers and in addition they have 50 parachutes for backup.

This relationship can be represented by a simple equation. Let P be the number of parachutes and S is the number of soldiers. Then we can represent the above relationship with the equation

P = 2 S + 50

From the above example we learned that an equation is a way of representing a relationship between variables. The variables in our example are P and S..


Depending on the form of the equation, i.e., the power of the variables, equations are given different names. We will learn about two kinds of equations, linear equations and quadratic equations in later pages.

Let us again consider the above example. If the number of soldiers is equal to 100, what would be the number of parachutes?
Finding the number of parachutes given the number of soldiers is called solving the equation.

A few hints for solving equations


y = ax + b is equivalent to y - b = ax.

That is, an equation does not change when we add or subtract the same term to both sides. In the example above we subtracted b from both sides.

y - b = ax is the same as ( y - b ) / a = x .

That is, an equation does not change if we multiply or divide both sides by the same term. In the above example we divided both sides by a.

y = xn is equivalent to y1/n = x.
That is, an equation does not change if we raise both sides to the same exponent. In the above example we raised both sides to 1/n.

Let us revisit our original problem now--


Number of soldiers S = 100
Number of parachutes P = 2 S + 50 = 2 x 100 + 50 = 250.