SOLUTION: What is the solution of the system of equations? 4x + y =14 5x + y = -11 is it consistant or inconsistent? is it independent or dependent?

Question 95734: What is the solution of the system of equations?
4x + y =14
5x + y = -11
is it consistant or inconsistent?
is it independent or dependent?
Found 2 solutions by checkley71, stanbon:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
4x+y=14 now now multiply the second equation by -1 & add.
-5x-y=11)
--------------------
-x=25
x=-25 answer.
4*-25+y=14
-100+y=14
y=14+100
y=114 answer.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What is the solution of the system of equations?
4x + y =14
5x + y = -11
--------------------
Let's assume the "x" in the two equations is the same and the "y"
in the two equations is the same.
--------------
Subtract the 1st equation from the 2nd to get:
x = -25
Substitute that in the 1st equation to solve for y:
4*-25 + y = 14
-100 + y = 14
y = 114
---------------------
So the assumption led to an acceptable answer.
Therefore the system is consistent.
If the assumption had led to a contrdiction
the system would be labeled inconsistent.
----------------------------
is it consistant or inconsistent?
is it independent or dependent?
The equations are independent; that means one is not
just a multiple of the other.
=====================
Cheers,
Stan H.
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