Consider the following system of equations.
y = 2x - 2
y - 2x = 7
What can you conclude about the system of equations?
The system of equations is inconsistent.
The system of equations is dependent.
The system of equations is independent.
none of these
since the slope is the same, they are either parallel or the same line. I expect you can decide which.
If parallel, no solutions, since they do not intersect.
If the same line, there are infinitely many solutions, since any point on one line is also on the other.
To determine what can be concluded about this system of equations, we need to solve the equations simultaneously and see if they have a unique solution, no solution, or infinitely many solutions.
First, let's solve the system of equations. We have the equations:
y = 2x - 2 (Equation 1)
y - 2x = 7 (Equation 2)
We can rearrange Equation 2 to isolate y:
y = 2x + 7
Now we can substitute this expression for y in Equation 1:
2x + 7 = 2x - 2
By subtracting 2x from both sides, we get:
7 = -2
Since 7 does not equal -2, we have a contradiction. This means there is no value of x and y that simultaneously satisfies both equations. Therefore, there is no unique solution, and the system of equations is inconsistent.
Therefore, the correct answer is: the system of equations is inconsistent.