### Edexcel GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# 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.
leading text: <span style="color: #
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.
leading text: <span style="color: #
V^2 = 64
*** QuickLaTeX cannot compile formula:
</span>
<span style="color: #000000;">
*** Error message:
You can't use macro parameter character #' in math mode.
leading text: <span style="color: #
V = \sqrt{64} = \pm8
*** QuickLaTeX cannot compile formula:
</span>
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<strong><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Example 7:</mark></strong>
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<mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Given
*** Error message:
Missing $inserted. a = 5b = 12x = \sqrt{a^2 + b^2} *** QuickLaTeX cannot compile formula: </mark> <!-- /wp:paragraph --> [bg_collapse view="button-blue" color="#fafafa" expand_text="Solution" collapse_text="Hide" ] <span style="color: #000000;"> *** Error message: Missing$ 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.
leading text: <span style="color: #
= \sqrt{169} = 13
*** QuickLaTeX cannot compile formula:
</span>
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<strong><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Example 8:</mark></strong>
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<mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Given
*** Error message:
Missing $inserted. u = 1v = 2z = 3a = 0b = 4w = u^2 + v^2 + z^2 + a^3 + b^3 *** QuickLaTeX cannot compile formula: </mark> <!-- /wp:paragraph --> [bg_collapse view="button-blue" color="#fafafa" expand_text="Solution" collapse_text="Hide" ] <span style="color: #000000;"> *** Error message: Missing$ 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.
leading text: <span style="color: #
w = 1 + 4 + 9 + 0 + 64
*** QuickLaTeX cannot compile formula:
</span>
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*** Error message:
You can't use macro parameter character #' in math mode.
leading text: <span style="color: #
w = 78
*** QuickLaTeX cannot compile formula:
</span>
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<strong><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Example 9:</mark></strong>
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<mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Given
*** Error message:
Missing $inserted. m = 100,000,000c = 300,000,000E = mc^2 *** QuickLaTeX cannot compile formula: </mark> <!-- /wp:paragraph --> [bg_collapse view="button-blue" color="#fafafa" expand_text="Solution" collapse_text="Hide" ] <span style="color: #000000;"> *** Error message: Missing$ 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.
leading text: <span style="color: #
E = 10^8 \times 3^2 \times 10^{16}
*** QuickLaTeX cannot compile formula:
</span>
<span style="color: #000000;">
*** Error message:
You can't use macro parameter character #' in math mode.
leading text: <span style="color: #
E = 9 \times 10^{24}\$