# Solving simultaneous equations with imaginary numbers

Consider the following simultaneous equation:

$$\begin{cases} 5z-(3+i)w=7-i\\ (2-i)z+2iw = -1+i \end{cases}$$

What is the simplest way to manipulate one of the equations so that a variable can be eliminated and the equation solved?

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You do it the same way you do it over the reals. For example, you could solve the first equation for $z$, $z=(7-i+(3+i)w)/5$, substitute that into the 2nd equation, solve for $w$, then get $z$. Or, multiply the first equation by $2-i$, the second by 5, and subtract to eliminate $z$.
I vote for multiplication by $2-i$ and $5$. –  James S. Cook Aug 26 '12 at 6:10
In this example, it looks like multiplying the second equation by $2+i$ might be easier. –  Mike Aug 26 '12 at 6:33