# Substituting Values into Formulae

In algebra, substitution involves replacing letters with numbers to calculate the value of an expression. A formula is a mathematical relationship connecting two or more quantities, such as , expressing F in terms of m and a.

Let’s look at some examples that involve substituting values into formulae and expressions.

## Examples

Example 1:

Given that and , find the value of the expression .

We substitute the values to find the expression’s value:  Example 2:

Given that and , find the value of F using   Example 3:

Given that , , and , find the value of x using the quadratic formula.  Example 4:

Find the value of T in the formula when , , and    Example 5:

Find the value of S in the formula when , , and    Example 6:

Given that , , and , find the possible values of V using *** QuickLaTeX cannot compile formula:
V^2 = 4^2 + 2(5)(4.8) = 16 + 10 \times 4.8</span>
<span style="color: #000000;">

*** Error message:
You can't use macro parameter character #' in math mode.


V^2 = 16 + 48
*** QuickLaTeX cannot compile formula:
</span>
<span style="color: #000000;">

*** Error message:
You can't use macro parameter character #' in math mode.


V^2 = 64
*** QuickLaTeX cannot compile formula:
</span>
<span style="color: #000000;">

*** Error message:
You can't use macro parameter character #' in math mode.


V = \sqrt{64} = \pm8
*** QuickLaTeX cannot compile formula:
</span>
[/bg_collapse]

<!-- wp:paragraph -->

<!-- /wp:paragraph -->

<!-- wp:paragraph -->

<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Example 7:</mark></strong>
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Given

*** Error message:
Missing $inserted.  a = 5 b = 12 x = \sqrt{a^2 + b^2} *** QuickLaTeX cannot compile formula: </mark> <!-- /wp:paragraph --> [bg_collapse view="button-blue" color="#fafafa" expand_text="Solution" collapse_text="Hide" ] <span style="color: #000000;"> *** Error message: Missing$ inserted.


x = \sqrt{5^2 + 12^2} = \sqrt{25 + 144}
*** QuickLaTeX cannot compile formula:
</span>
<span style="color: #000000;">

*** Error message:
You can't use macro parameter character #' in math mode.


= \sqrt{169} = 13
*** QuickLaTeX cannot compile formula:
</span>
[/bg_collapse]

<!-- wp:paragraph -->

<!-- /wp:paragraph -->

<!-- wp:paragraph -->

<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Example 8:</mark></strong>
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Given

*** Error message:
Missing $inserted.  u = 1 v = 2 z = 3 a = 0 b = 4 w = u^2 + v^2 + z^2 + a^3 + b^3 *** QuickLaTeX cannot compile formula: </mark> <!-- /wp:paragraph --> [bg_collapse view="button-blue" color="#fafafa" expand_text="Solution" collapse_text="Hide" ] <span style="color: #000000;"> *** Error message: Missing$ inserted.


w = 1^2 + 2^2 + 3^2 + 0^3 + 4^3
*** QuickLaTeX cannot compile formula:
</span>
<span style="color: #000000;">

*** Error message:
You can't use macro parameter character #' in math mode.


w = 1 + 4 + 9 + 0 + 64
*** QuickLaTeX cannot compile formula:
</span>
<span style="color: #000000;">

*** Error message:
You can't use macro parameter character #' in math mode.


w = 78
*** QuickLaTeX cannot compile formula:
</span>
[/bg_collapse]

<!-- wp:paragraph -->

<!-- /wp:paragraph -->

<!-- wp:paragraph -->

<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Example 9:</mark></strong>
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Given

*** Error message:
Missing $inserted.  m = 100,000,000 c = 300,000,000 E = mc^2 *** QuickLaTeX cannot compile formula: </mark> <!-- /wp:paragraph --> [bg_collapse view="button-blue" color="#fafafa" expand_text="Solution" collapse_text="Hide" ] <span style="color: #000000;"> *** Error message: Missing$ inserted.


E = mc^2 = 10^8 \times (3 \times 10^8)^2
*** QuickLaTeX cannot compile formula:
</span>
<span style="color: #000000;">

*** Error message:
You can't use macro parameter character #' in math mode.

*** QuickLaTeX cannot compile formula:
You can't use macro parameter character #' in math mode.