# How do you write a system of equations?

##### 1 Answer

#### Answer:

Any set of equations is a system of equations. Whether it has solutions, let alone a unique solution is another question.

#### Explanation:

Playing with the question a little, given a solution in a number of variables, how do you create a set of equations to which they are the unique solution?

For example: Start with:

How do we generate a system of equations for which this is the only solution?

**Option A:** Do nothing. This is a set of equations with the desired unique solution. Downside: too obvious.

**Option B:** Since there are

This generally works well, except that we can create a set of equations that have multiple solutions. For example, if we chose

To avoid this, just try solving the question you create.

**Option C:** Go beyond linear. Plenty of scope for imagination here.

For example:

Downside: You will probably introduce additional unexpected irrational and/or complex solutions.