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

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) (Show Source): You can put this solution on YOUR website!

Start with the second equation

Plug in . In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute

Combine like terms on the left side

Subtract 9 from both sides

Combine like terms on the right side

Now that we know that , we can plug this into to find

Substitute for each

Add

So the solutions are and 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 (red) and (green)

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