Solving simultaneous equations by substitution

If you have two variables in an equation then you cannot hope to solve it. There are two things you don't know, but only one piece of information about them.

In this case you need more equations - you need as many equations as you have unknown variables.

If the equations are linear then they are best handled by matrix techniques - see here.

There is a general technique that works well provided that you can manipulate at least one equation into the form y=f(x).

For example, suppose that we want to solve the following two equations. One is a line and the other a quadratic - a parabola. We will find where the line and the parabola intersect. -mathformula not MarkupType-
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