SOLUTION: x=y+3 3x-2y=4. I did get to work this problem out and hopefully it is right but I do not know if it is independent, dependent or inconsistent. I solved by substitution and think i

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: x=y+3 3x-2y=4. I did get to work this problem out and hopefully it is right but I do not know if it is independent, dependent or inconsistent. I solved by substitution and think i      Log On


   

Question 173080: x=y+3 3x-2y=4. I did get to work this problem out and hopefully it is right but I do not know if it is independent, dependent or inconsistent. I solved by substitution and think it is I thought it was onconsistent but somebody told me I was incorrect. Can you explain the difference and what it is? Tyvm, Judy
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x-2y=4 Start with the second equation


3%28y%2B3%29-2y=4 Plug in x=y%2B3. In other words, replace each x with y%2B3. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


3y%2B9-2y=4 Distribute


y%2B9=4 Combine like terms on the left side


y=4-9Subtract 9 from both sides


y=-5 Combine like terms on the right side




Now that we know that y=-5, we can plug this into x=y%2B3 to find x



x=%28-5%29%2B3 Substitute -5 for each y


x=-2 Add


So the solutions are x=-2 and y=-5 which form the ordered pair


Since the system has a unique solution, this means that the system is consistent and independent.


Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.
Graph of 3x-2y=4 (red) and x=y%2B3 (green)