# Systems of Linear Equations

## Systems of Linear Equations

Systems of linear equations can be solved with arrays and NumPy. A system of linear equations is shown below:

8x + 3y -2z = 9
-4x + 7y + 5z = 15

$$3x + 4y - 12z = 35$$ NumPy's np.linalg.solve() function can be used to solve this system of equations for the variables $x$, $y$ and $z$.

The steps to solve the system of linear equations with np.linalg.solve() are below:

• Create NumPy array A as a 3 by 3 array of the coefficients
• Create a NumPy array b as the right-hand side of the equations
• Solve for the values of $x$, $y$ and $z$ using np.linalg.solve(A, b).

The resulting array has three entries. One entry for each variable.

In [1]:
import numpy as np

A = np.array([[8, 3, -2], [-4, 7, 5], [3, 4, -12]]) b = np.array([9, 15, 35]) x = np.linalg.solve(A, b) x

Out[1]:
array([-0.58226371,  3.22870478, -1.98599767])

We can plug the valuse of $x$, $y$ and $z$ back into one of the equations to check the answer.

$x$ is the first entry of the array, $y$ is the second entry of the array, and $z$ is the third entry of the array.

$x$ = x[0]

$y$ = x[1]

$z$ = x[2]

When these values are plugged into the equation from above:

8x + 3y -2z = 9

The answer should be 9.0.

In [2]:
8*x[0] + 3*x[1] - 2*x[2]
Out[2]:
9.0