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How do I solve a simultaneous equation with more unknowns than equations?

If a set of equations has more unknowns than equations, you cannot get a value for each unknown. However, you can find the relationships between the variables.

Start by rearranging one variable in terms of the others and then plug that equation into the others, eliminating one variable. You will then be able to link the rest of the variables together in terms of each other.

Finally, set one variable as a parameter, say u, and give the values of all the variable in terms of that uniting parameter.

For example, you will end up with something like:

x = 2u - 1

y = 1/2u + 4

z = u

Hayden M. A Level Further Mathematics  tutor, GCSE Maths tutor, A Lev...

2 years ago

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