👉 Simultaneous Equations Solver

Simple tool to solve systems of equations

ℹ️ Requirements

• Numpy (for solving using matrices)
• String (native Python module)

💡 How it works

• Systems of equations can be modelled as matrices in order to solve them
• The concept and example illustrated below explain the calculations that occur:

$$ A \begin{bmatrix} x \\ y \\ z \end{bmatrix} = C $$

$$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} = A^{-1} C $$

Example

$$ 3x+2y-z=11 $$

$$ 2x-3y+z=7 $$

$$ 5x+y-2z=12 \ $$

$$ \therefore \begin{bmatrix} 3 & 2 & -1 \\ 2 & -3 & 1\\ 5 & 1 & -2 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 11 \\ 7 \\ 12 \end{bmatrix} \\ $$

$$ \therefore \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 3 & 2 & -1 \\ 2 & -3 & 1\\ 5 & 1 & -2 \end{bmatrix}^{-1} \begin{bmatrix} 11 \\ 7 \\ 12 \end{bmatrix} = \begin{bmatrix} 4 \\ 2 \\ 5 \end{bmatrix} \\ $$

Solutions

$$ x=4 \ $$

$$ y=2 \ $$

$$ z=5 $$

👎 Limitations

• Only supports three variables at the moment
• Doesn't currently support float inputs