## 2. Inconsistent Systems ##

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0,20,1000)
y1 = -2*x + 5/4
y2 = -2*x + 5/2

plt.plot(x,y1,color="blue")
plt.plot(x,y2,color="blue")
plt.show()

## 5. Homogenous Systems ##

def test_homog(x3):
    x1 = (4/3)*x3
    x2 = 0
    eqn1 = (6*x1 + 10*x2 + -8*x3 == 0)
    eqn2 = (-6*x1 + -4*x2 + 8*x3 == 0)
    eqn3 = (3*x1 + 0.5*x2 + -4*x3 == 0)
    if (eqn1 and eqn2 and eqn3):
        return True
    else:
        return False
    
b_one = test_homog(1)
b_two = test_homog(-10)