Consider the following system of equations.
Y = 3x – 7
Y - 3x = 5
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
To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, we can use a method called the elimination method.
The elimination method involves manipulating the equations to eliminate one variable and solve for the other variable. In this case, we can eliminate the variable y by subtracting the second equation from the first equation.
Let's perform this elimination:
Y = 3x – 7
Y - 3x = 5
-----------------
0 = -12
After subtracting the second equation from the first equation, we are left with the equation 0 = -12.
This equation indicates that 0 is equal to -12, which is not true. Therefore, the system of equations is inconsistent.
Therefore, the correct answer is:
a) The system of equations is inconsistent.