# 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 ->  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

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 Click here to see ALL problems on Linear-equations 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 = -20Answer by venugopalramana(3286)   (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