如何使用Python解决2个未知数的一个线性代数方程

Question

Trying to solve problem of 2 investments with 2% and 4% annual interest respectively. If $10,000 total was originally invested and the account had $10,250 at year end, what was the principal in each investment. I've tried using the solve function

This is the equation I came up with to represent the problem. 1.04x+1.02y=10000 * 1.025

However I'm not sure that I'm properly placing the coefficients into the arrays.

This is the code I set up:

import numpy as np

A = np.array([[1.0,1.0],[104,102]])
Y = np.array([[1.025],[10000.0]])
np.linalg.solve(A, Y) 

I'd expect the results to be $7500 and $2500 which satisfy the equation and up to $10,250, however running my code I get:

array([[ 4947.725],
       [-4946.7  ]])

Answer 1

I think you misswrote your matrix system:

import numpy as np

A = np.array([[1.0,1.0],[1.04,1.02]])
Y = np.array([[10000.0],[10250.0]])
np.linalg.solve(A, Y)
>>>array([[2500.], [7500.]])

Which is what you expected