Elementary algebra
Elimination method

An example of solving a system of linear equations is by using the elimination method:

Multiplying the terms in the second equation by 2:

Adding the two equations together to get:

which simplifies to

Since the fact that x = 2 {\displaystyle x=2} is known, it is then possible to deduce that y = 3 {\displaystyle y=3} by either of the original two equations (by using 2 instead of x) The full solution to this problem is then

This is not the only way to solve this specific system; y could have been resolved before x.
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