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# Substituting into Formulae

In algebra, substitution is putting numbers in place of letters to calculate the value of an expression. For example:

If e=3 and f=4. what is that value of ?

40ef is the same as writing multiplied by multiplied by .

First of all, as we know that e=3, we replace e with 3 in the expression and we are left with: 40 multiplied by 3 multiplied by f.

Likewise, we do the same with f. We replace f with 4 in the expression and we are left with: 40 multiplied by 3 multiplied by 4.

Therefore, .

A formula is a mathematical relationship connecting two or more quantities. For example, , expressing F in terms of m and a.

is a formula giving x in terms of the quantities of a, b and c.

From F=ma, we can find the value of F if we are given values for m and a, which you can see in the example below.

## Example

Find the value of F if and

## Example

From the formula , if we are given that a = 2, b = 5 and c = −12, find the value of x.

We know that a=2, b=5 and c=−12, so:

## Example

Find the value of T when , and , that:

.

Substituting , and gives:

## Example

Find the value of S if:

When , and .

## Example

Given that . Find the possible values of V when u = 4, a = 5 and S = 4.8

Substituting , and into the formula gives us:

## Example

Find the possible values of x if , when and

So, we will use the formula

Substituting and gives us:

## Example

Find the value of w if if:

.

We substitute u=1, v=-2, z=-3, a=0 and b=4 into the formula to get:

## Example

Evaluate y in each of the following expressions, given that:

, and

i)

ii)

iii)

iv)

v)

i)

ii)

iii)

iv) y = \frac{x+z+w}{xzw}

= \frac{2+3-1}{2(3)(-1)}

= \frac{4}{-6}

= \frac{-2}{3}

v)

*** QuickLaTeX cannot compile formula:
<span style="color: #000000;">= \frac{2(3)(-1)}{2+3-1}

*** Error message:
You can't use macro parameter character #' in math mode.
leading text: $<span style="color: #  *** QuickLaTeX cannot compile formula: <span style="color: #000000;">= \frac{-6}{4} *** Error message: You can't use macro parameter character #' in math mode. leading text:$<span style="color: #



## Example

Find the value of w when:

, , and

Substituting , and into the formula gives:

## Example

Giving that . Find the value of E when and , giving an answer in standard form.

Substituting , in gives:

*** QuickLaTeX cannot compile formula:
= { 10 }^{ 8 } \times { 3 }^{ 2 } \times ({ 10 }^{ 8 }) }^{ 2 }

*** Error message:
Extra }, or forgotten \$.
leading text: ... \times { 3 }^{ 2 } \times ({ 10 }^{ 8 }) }



## Example

Find the value of x if and , given that

We substitute and into the formula, which gives us: