Question

If 5x + 7y is even, then prove both x and y are even or both x and y are odd

Answer 1

★ THEORY OF NUMBERS ★

Consider (n) to be even , then (n + 1) is obviously odd

x = n [ even ]

y = n + 1 [ odd ]

Now , verification ,

5x + 7y is even

For x = n , y = n [ simultaneously ]

5 ( n ) + 7 ( n ) = 12 ( n )

even multiple , Hence an even format proved

Again ,

5 ( n + 1 ) + 7 ( n + 1 ) = 12 ( n + 1 )

Hence , again an even multiple format

It's proved entirely by the above results that , 5x + 7y is even , if simultaneously x and y are either both even or odd

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