SOLUTION: Solve the system of equations using either the substitution or the elimination method. If there is a unique solution present it as an ordered Pair adn show the check of your soluti

Question 21350: Solve the system of equations using either the substitution or the elimination method. If there is a unique solution present it as an ordered Pair adn show the check of your solution. If there is no unique solution state why and show how you determined your answer. x = 6-3y and 2x +6y=12
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Solve the system of equations using either the substitution or the elimination method. If there is a unique solution present it as an ordered Pair adn show the check of your solution. If there is no unique solution state why and show how you determined your answer. x = 6-3y and 2x +6y=12
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X=6-3Y..OR....X+3Y=6.................I
2X+6Y=12................................II
II/2...GIVES US .......X+3Y=6..................III
WE FIND THE 2 EQUATIONS GIVEN ARE SAME OR LINEARLY DEPENDENT..ONE IS OBTAINED BY MULTIPLYING WITH 2 THE OTHER....SO WE HAVE IN EFFECT GOT ONLY ONE INDEPENDENT EQN.WITH 2 UNKNOWNS WHICH GIVES RAISE TO INFINITE SOLUTIONS....
FOR EXAMPLE IF WE PUT X=0 WE GET Y =2..WE CAN TABULATE AS BELOW...
X...0.....3.......6.......ETC.....
Y...2.....1.......0........ETC.....
PLEASE NOTE..... THOUGH THERE ARE INFINITE SOLUTIONS IT DOES NOT MEAN ALL OR ANY VALUE OF X AND Y ..A SET OF VALUES FOR X AND Y ONLY ARE CORRECT THOUGH THEY ARE INFINITE IN NUMBER THEY DO NOT REPRESENT ALL OR EVERY VALUE...
TO SHOW YOU THE DIFFERENCE THE IDENTITY...........
(X+Y)^2=X^2+Y^2+2XY....IS AN IDENTITY WHICH IS AGAIN TRUE FOR INFINITE VALUES OF X AND Y BUT THIS TIME FOR ANY ND EVERY VALUE OF X AND Y...HENCE IT IS CALLED AN IDENTITY OR CONGRUENCE , WHERE AS YOUR PROBLEM IS AN EQUALITY NOT AN IDENTITY...
I WENT BEYOND YOUR QUESTION TO POINT OUT THE DIFFERENCE BETWEEN AN EUATION AND IDENTITY AND THE FACT THAT INFINITY DOES NOT MEAN EVERY THING.
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