# How to Solve a System of Equations in Python (3 Examples)

To solve a system of equations in Python, we can use functions from the NumPy library.

The following examples show how to use NumPy to solve several different systems of equations in Python.

### Example 1: Solve System of Equations with Two Variables

Suppose we have the following system of equations and we’d like to solve for the values of x and y:

5x + 4y = 35

2x + 6y = 36

The following code shows how to use NumPy to solve for the values of x and y:

```import numpy as np

#define left-hand side of equation
left_side = np.array([[5, 4], [2, 6]])

#define right-hand side of equation
right_side = np.array([35, 36])

#solve for x and y
np.linalg.inv(left_side).dot(right_side)

array([3., 5.])
```

This tells us that the value for x is 3 and the value for y is 5.

### Example 2: Solve System of Equations with Three Variables

Suppose we have the following system of equations and we’d like to solve for the values of x, y, and z:

4x + 2y + 1z = 34

3x + 5y – 2z = 41

2x + 2y + 4z = 30

The following code shows how to use NumPy to solve for the values of x, y, and z:

```import numpy as np

#define left-hand side of equation
left_side = np.array([[4, 2, 1], [3, 5, -2], [2, 2, 4]])

#define right-hand side of equation
right_side = np.array([34, 41, 30])

#solve for x, y, and z
np.linalg.inv(left_side).dot(right_side)

array([5., 6., 2.])
```

This tells us that the value for x is 5, the value for y is 6, and the value for z is 2.

### Example 3: Solve System of Equations with Four Variables

Suppose we have the following system of equations and we’d like to solve for the values of w, x, y, and z:

6w + 2x + 2y + 1z = 37

2w + 1x + 1y + 0z = 14

3w + 2x + 2y + 4z = 28

2w + 0x + 5y + 5z = 28

The following code shows how to use NumPy to solve for the values of w, x, y, and z:

```import numpy as np

#define left-hand side of equation
left_side = np.array([[6, 2, 2, 1], [2, 1, 1, 0], [3, 2, 2, 4], [2, 0, 5, 5]])

#define right-hand side of equation
right_side = np.array([37, 14, 28, 28])

#solve for w, x, y, and z
np.linalg.inv(left_side).dot(right_side)

array([4., 3., 3., 1.])
```

This tells us that the value for w is 4, x is 3, y is 3, and z is 1.