GCSE Maths

Simultaneous Equations 2

So far so good! Let's look at a harder example:

2a + b = 21
a + b = 15

In this case we cannot just solve for a or b individually, as both variables appear in each equation. Instead we must rearrange an equation to find an unknown in terms of the other:

b = 15 - a
[This is the second equation re-stated]

Now we can substitute this statement for b into the first equation:

2a + b = 21
2a + (15 - a) = 21

This can now be tidied up, giving a correct answer for a:

2a - a = 21 - 15
a = 6

Finally we can use any of the first 3 equations to find b:

b = 15 - 6
b = 9


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