> For the complete documentation index, see [llms.txt](https://jona-projects.gitbook.io/kiwicalc/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jona-projects.gitbook.io/kiwicalc/systems-of-equations/systems-of-polynomial-equations.md).

# Systems of Polynomial Equations

#### Systems of polynomial equations

You can solve a system of polynomial equations using the solve\_poly\_system method. Further elaboration on the method is written on the numerical methods section of this documentation. Here is an example of using the method to find the solutions of the system: 

$$
\left{
\begin{array}{l}
x^2 + y^2 = 25 \\
2x + 3y = 18
\end{array}
\right.
$$

 with the initial guess:

$$
X\_0 =
\begin{bmatrix}
2 \\
1
\end{bmatrix}
$$

```
 # Solving systems of polynomial equations via KiwiCalc
solutions = solve_poly_system(["x^2 + y^2 = 25", "2x + 3y = 18"], {'x': 2, 'y': 1})
print(solutions)
# output: '{'x': 3.0000001628514434, 'y': 3.999999891432371}'
                    
```

Specifying an initial guess is only optional and can help reduce the runtime of the method.