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Engineering Formulae


We will focus here in the application of basic algebra to engineering problems.

In algebra, letters or symbols are used to represent numbers.

These letters or symbols may be constants, that is fixed, or variables, which means they can take up various values.


Transposition of Formulae

In the formula


y = a + bx


we say y is the subject of the formula.

If we want to make x the subject of the formula then we need to change the form to  




 This process of changing the subject is called transposition of formulae.


Equations are made up of mathematical expressions in which there are one or more unknown quantities.

Equations arise in engineering problems when the underlying laws or physical principles

are applied to model the problems.

To solve an equation means finding the unknown quantities.

There are many types of equations and the solution of these equations is tackled in different ways.


Linear Equations


A linear expression a mathematical statement that performs functions of addition, subtraction, multiplication, and division, but has no exponents or power.

A linear equation is a mathematical expression that has an equal sign and linear expressions.

It is an equation of the form





where a and b are known numbers, and x is unknown quantity that we must find.

In the above equation

the number a is called the coefficient of x, and the number b is called the constant term.


Example 1: Which of the following are linear equations and which are not linear?


Solution: The equations that can be written in the form ax + b = 0 are linear.


4x + 8 = 0

Linear; it is written in the form of a standard equation

6x2 + 6 = 0

Nonlinear; because of the term x2

4x = 0

Linear; the constant term is zero



Solving Linear Equations


To solve a linear equation means to find the value of x that can be substituted into the equation so that the left-hand side equals the right-hand side.

Any such value is known as a solution or root of the equation.

If a number is a root, we say that it satisfies the equation.


Example 2: Test which of the following values are solutions of the equation




 (a) x = 2,   (b) x = 3,   (c) x = 8




(a)     Substitute x = 2, the left hand side equals 8; 10 is not equal to 8, so x = 2 is not a solution.

(b)     Substitute x = 3, the left hand side equals 10; this is the same as the right hand side, so x = 3 is a solution.

(c)     Substitute x = 8, the left hand side equals 20; 20 is not equal to 8, so x = 8 is not a solution.