Consider the following system of equations.
y = 4x - 4
y - 4x = 3
What can you conclude about the system of equations?
A) The system of equations is inconsistent.
B) The system of equations is dependent.
C) The system of equations is independent.
D) none of these
4x -4 = 4x + 3
4x -4x = 3+ 4
0 = 7
A
To determine the nature of the system of equations, we can analyze the coefficients of the variables.
In this case, we have:
Equation 1: y = 4x - 4
Equation 2: y - 4x = 3
Comparing the coefficients of x in both equations, we see that they are both 4.
Comparing the coefficients of y in both equations, we see that it is 1 in Equation 1 and 1 in Equation 2.
Since the coefficients of both x and y are the same in both equations, the system of equations is dependent.
Therefore, the correct answer is:
B) The system of equations is dependent.