what can u conclude about the system of equations

Question

Y=3x-7

Y-3x=5

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

 

Answer 1

A. The system of equations is inconsistent, that is, it has no solution in R. 

Answer 2

Change the second equation to slope-intercept form:

 

Y-3x=5

y = 3x + 5

 

So the lines for both equations have the same slope, but different intercepts.  Therefore they are parallel and do not intersect.  Therefore the system is inconsistent.  Any values of x and y that satisfy one equation do NOT satisfy the other.