SOLUTION: Solve each system by addition.As part of your answer indicate whether the equation are independent, dependent, or inconsistent. x-y=3 -6x+6y=17

Question 206059: Solve each system by addition.As part of your answer indicate whether the equation are independent, dependent, or inconsistent.
x-y=3
-6x+6y=17
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve each system by addition.As part of your answer indicate whether the equation are independent, dependent, or inconsistent.
x-y=3
-6x+6y=17
-------------------------------------
Multiply thru the 1st equation by 6 to get:
6x-6y = 18
---
Add that to the 2nd equation to get:
0 = 35
--------------------
That is a contradictin that happened because we assumed
the "x" in both equations and the "y" in both equations
had a consistent meaning.
---
They do not so the system of equations is said to be
inconsistent.
========================================
Cheers,
stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the first equation by 6.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Since is never true, this means that there are no solutions.

So the system is inconsistent.

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