SOLUTION: Solving systems by graphing and substitution 3x - y = 4 3x - y = 0 Please show me if this problem is independent, dependent or inconsistent. More importantly I'd like to kno

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solving systems by graphing and substitution 3x - y = 4 3x - y = 0 Please show me if this problem is independent, dependent or inconsistent. More importantly I'd like to kno      Log On


   

Question 390608: Solving systems by graphing and substitution
3x - y = 4
3x - y = 0
Please show me if this problem is independent, dependent or inconsistent. More importantly I'd like to know the best way to solve future problems like this''.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If you get both equations into the form
y+=+mx+%2B+b, and graph both, you can
see slopes, m, and y-intercepts, b.
3x+-+y+=+4
add y to both sides
3x+=+y+%2B+4
Subtract 4 from both sides
3x+-+4+=+y
Swap left and right sides
y+=+3x+-+4
------------
3x+-+y+=+0
Add y to both sides
3x+=+y
Swap sides
y+=+3x
---------
Now I'll plot them
+graph%28+400%2C+400%2C+-8%2C+8%2C+-10%2C+10%2C++3x-4%2C3x%29+
As you can see, they are parallel lines, both with m+=+3,
so there can be no solution. Even if the slopes were
slightly different, say 3 and 3.00001, there would be a solution
since they would have to meet somewhere.
these equations are inconsistant