3.1 Algebraic Formulae - Mathematics

3.1 Algebraic Formulae

3.1.1 Variables and Constant

1. A variable is a quantity without a fixed value.

2. A constant is a quantity with a fixed value.

3.1.2 Concept of Formulae

1. An algebraic formula is an equation which shows the relationship between several variables and/ or constant.

2. The subject of an algebraic formula is a linear variable expressed in terms of the other variables.

Example 1:

Express x in terms of y, if y = \frac{2 - 3 x}{x} .

$Express x in terms of y, if y = \frac{2 - 3 x}{x} .$

Solution:

\begin{array}{l} y = \frac{2 - 3 x}{x} \\ x y = 2 - 3 x \\ x y + 3 x = 2 \\ x (y + 3) = 2 \\ x = \frac{2}{y + 3} \end{array}

$\begin{array}{l} y = \frac{2 - 3 x}{x} \\ x y = 2 - 3 x \\ x y + 3 x = 2 \\ x (y + 3) = 2 \\ x = \frac{2}{y + 3} \end{array}$

Example 2:

Given that s = \frac{p^{2} - q^{2}}{2 u}, make p the subject of the formula .

$Given that s = \frac{p^{2} - q^{2}}{2 u}, make p the subject of the formula .$

Solution:

\begin{array}{l} s = \frac{p^{2} - q^{2}}{2 u} \\ 2 u s = p^{2} - q^{2} \\ p^{2} = 2 u s + q^{2} \\ p = \sqrt{2 u s + q^{2}} \end{array}

$\begin{array}{l} s = \frac{p^{2} - q^{2}}{2 u} \\ 2 u s = p^{2} - q^{2} \\ p^{2} = 2 u s + q^{2} \\ p = \sqrt{2 u s + q^{2}} \end{array}$