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Substitution

GCSELevel 4-5AQAEdexcelOCRWJEC

Substitution Revision

Substitution

Substitution means replacing letters or symbols in algebraic equations or expressions with numbers to find out their total value.

Level 4-5GCSEAQAEdexcelOCRWJEC

Using Substitution

Substitution can be helpful in utilising formulae and equations. 

For example, we know

\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}

To utilise this helpful equation, we need to use substitution:

It takes Esme 45\text{ minutes} to travel to school, which is 3\text{ km} away. We can use substitution into the equation above the find the speed Esme travels in \text{km/h}:

Distance = 3\text{ km}

Time = 0.75\text{ hours}

\text{Speed} = \dfrac{3}{0.75}

\text{Speed} = 4\text{ km/h}

Level 4-5GCSEAQAEdexcelOCRWJEC
Level 4-5GCSEAQAEdexcelOCRWJEC

Example 1

Given

k = 5a + 19b - 12c - \dfrac{d}{4}

Work out the value of k when 

a=8\\ b=2\\ c=4\\ d=48

[2 marks]

Substituting the values of a, b, c, and d into the equation:

k = 5\times8 + 19\times2 - 12\times4 - \dfrac{48}{4}

You must remember BIDMAS when using substitution, so division/multiplication must come before addition/subtraction.

k = 40 + 38 - 48 - 12

k =18

Level 4-5GCSEAQAEdexcelOCRWJEC

Example 2

Using the quadratic formula is an example of substitution

Given the quadratic formula

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

Solves equations in the form

ax^2+bx+c=0

Use substitution into the quadratic formula to solve

3x^2+5x+2=0

[3 marks]

We can see from the equation that:

a=3\\ b=5\\ c=2

So, we can substitute these into the quadratic equation:

x=\dfrac{-5\pm\sqrt{5^2-4(3)(2)}}{2(3)}

Which gives us the solutions x=-\dfrac{2}{3} and x=-1

 

Level 4-5GCSEAQAEdexcelOCRWJEC

Substitution Example Questions

If a=36, b=\dfrac{1}{2}(36) = 18

Substitution:

Z=2(36)+5(18)^3\\ Z=29232
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Substitution:

46 = 5m + 16

Rearrange and solve:

46-16=5m\\ 30=5m\\ m=6
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Substitution:

y = 2(78)-21\\ y = 135

Ezra would be expected to score 135 in his English test.

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