# How do you solve the simultaneous equations #x^2 + y^2=29# and #y-x=3#?

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Use the second equation to provide an expression for

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First add

Then substitute this expression for

Subtract

Divide both sides by

So

If

If

So the two solutions

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Since you have both

You want to combine these two equations into one equation with a single variable, solve it and then solve for the other variable. An example on how to do this goes like this:

Since

We can solve for

So

Since

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