**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.

4*x* + 8 =
0 |
Linear; it is written in the form of a standard
equation |

6*x*^{2
}+ 6 = 0 |
Nonlinear; because of the term *x*^{2} |

4*x* = 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

**
Solution**

(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.