 # Python – How to Solve Simultaneous Equations

## Introduction

Python in combination with Numpy allows for using python to solve simultaneous equations in a few simple steps. Using python to solve simultaneous equations relies on matrix linear algebra and can be done by using a built-in function (method 1) or manually (method 2) manually manipulating the matrices  to solve.

So how to solve simultaneous equations with python? For our example we will be using the following two equations:

5x + 3y =40

x + 2y = 18

## Method 1

Step 1

Convert the system of equations to matrix form:

For our example we have: Step 2

Import the numpy module and write the matrices as numpy arrays.

` import numpy as np`

Step 3

Define coefficient and results matrices as numpy arrays

` A = np.array([[5,3],[1,2]])`
` B = np.array([40,18])`

Step 4

Use numpy’s linear algebra solve function to solve the system

` C = np.linalg.solve(A,B)`

C is now an array with the value of the variables. Type C and press enter to see the values, this is how method 1 solves simultaneous equations.

` print C`
```[ 3.71428571,  7.14285714]
```

Full code

```import numpy as np
A = np.array([[5,3], [1,2]])
B = np.array([40,18])
C = np.linalg.solve(A, B)
print C```

## Method 2

Step 1

Convert the system of equations to matrix form:

For our example we have: Step 2

Import the numpy module and write the matrices as numpy arrays.

`import numpy as np`

Step 3

Define coefficient and results matrices as numpy arrays

`A = np.array([[5,3],[1,2]])`
` B = np.array([40,18])`

Step 4

Use numpy’s linear algebra inv function to find the inverse of matrix A

`D = np.linalg.inv(A)`

Step 5

Use numpy’s dot function to find the dot product of the inverse of the coefficient matrix and the results matrix

`E=np.dot(D,B)`

E is now an array with the value of the variables. Type E and press enter to see the values.

`E`
`array([ 3.71428571,  7.14285714])`

Full Code

```import numpy as np
A = np.array([[5,3], [1,2]])
B = np.array([40,18])
D = np.linalg.inv(A)
E = np.dot(D,B)
print E```

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