Introducing simultaneous equations

We have looked at how to solve equations with one unknown value, but what happens when there are two unknown values?

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Equations with more than one value to be found are called simultaneous equations.

When there are two unknown values, then two equations will be required in order to solve them.

The two equations cannot be solved on their own. Each one by itself has infinitely many solutions.

For example x + y = 10 has infinitely many values for x and y for which this is true, such as:

x=1, y=9

or x=10, y=0

or x=100, y=-90, etc

But you can use two equations together to make one equation that has only one solution. The x and y values of this solution will solve both of the original equations at the same time. This is why they are called simultaneous equations - because you are trying to solve them both with the same values for x and y.