A seven, a three and 2016!?
7 x − 3 y = 2 0 1 6
How many real solutions (ordered pairs) satisfy the equation above?
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1 solution
Can you explain a little how real solutions will yield infinite solution?
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3 y = m ( m shall be positive integer, to make things easier).
Then 7 x = 2 0 1 6 + m
y = lo g 3 m and x = lo g 7 ( 2 0 1 6 + m )
So if m = 1 then: ( x , y ) = ( lo g 7 2 0 1 7 , 0 ) , both values are real.
That applies for m = 2 , 3 , 4 , . . . . . . to the infinity.
Solution:
This one is more of a trick than a real problem. Since it says " real solutions " and not integers , number of ordered pairs that satisfy the equation is ∞ .