SOLUTION: . Solve the following system by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. x + 5y = 10 -2x – 10y = -20

Algebra ->  Linear-equations -> SOLUTION: . Solve the following system by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. x + 5y = 10 -2x – 10y = -20      Log On


   

Question 36728: . Solve the following system by addition. If a unique solution does not exist, state
whether the system is inconsistent or dependent.
x + 5y = 10
-2x – 10y = -20
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
. Solve the following system by addition. If a unique solution does not exist, state
whether the system is inconsistent or dependent.
x + 5y = 10...................................................I
-2x – 10y = -20.................................II
-2*EQN.I GIVES
-2X-10Y=-20....WHICH IS SAME AS EQN.II...
HENCE THEY ARE DEPENDENT EQUATIONS.
SO INEFFECT WE HAVE ONLY ONE EQN.TO SOLVE FOR 2 UNKOWNS.
HENCE WE SHALL HAVE INFINTE SOLUTIONS LIKE IN THIS CASE
X=0....Y=2
X=10...Y=0...ETC..
IMPORTANT NOTE.
THEY HAVE INFINITE SOLUTIONS BUT NOT ANY AND EVERY VALUE OF X AND Y.FOR EXAMPLE IF X=0 ,THEN Y HAS TO EQUAL 2 ONLY NOT ANY OTHER VALUE.SO IT HAS INFINITE SETS OF X AND Y PAIRS FOR ITS SOLUTION