### Requirements

If you have not yet installed HomotopyContinuation.jl, please consider the installation guide.

### Solve your first system of equations

Consider the following simple system of two polynomials in two variables.

$$ f=\begin{bmatrix}x^2+2y \\ y^2-2 \end{bmatrix} $$

Solving the equation $f=0$ can be accomplished as follows

```
using HomotopyContinuation # load the package into the current Julia session
@var x y; # declare the variables x and y
f = System([x^2 + 2y, y^2 - 2]) # construct system f
result = solve(f) # solve f
```

After the computation has finished, you should see the following output.

```
Result with 4 solutions
=======================
• 4 paths tracked
• 4 non-singular solutions (2 real)
• random seed: 0x09c7d125
• start_system: :polyhedral
```

We see that $f$ has two real zeros. They are

```
julia> realsolutions(result)
2-element Array{Array{Float64,1},1}:
[1.68179, -1.41421]
[-1.68179, -1.41421]
```

It is possible to interrupt the computations using `ctrl+c`

. All solutions that have been computed before the interruption will be returned.

### What else should I know?

The next guide explains in greater detail how to use HomotopyContinuation.jl. You should also check the rest of our detailed Guides for learning more about the full power of homotopy continuation. Furthermore, our Reference documentation lists all options of `solve(f)`

.