document.write( "Question 1194179: If 5x-y is divisible by 4 and 2x+3y is odd. Then 7x+2y is odd for all x,y ∈Z. \n" ); document.write( "

Algebra.Com's Answer #826317 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "If 5x-y is divisible by 4 and 2x+3y is odd. Then 7x+2y is odd for all x,y ∈Z.
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\n" ); document.write( "\n" ); document.write( " To be mathematically correct (and do not scare readers), the statement needs to be modified.\r
\n" ); document.write( "\n" ); document.write( " The modified version is THIS :\r
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document.write( "                If x and y are integer numbers such that 5x-y is divisible by 4 and 2x+3y is odd, then 7x+2y is odd.\r\n" );
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\n" ); document.write( "\n" ); document.write( " Below is my solution for this modified version.\r
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document.write( "Since 2x + 3y is odd, it means that 3y is odd.\r\n" );
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document.write( "In turn, it means that y is odd.\r\n" );
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document.write( "Next, 5x-y is divisible by 4.  It implies that x-y is divisible by 4.\r\n" );
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document.write( "Since y is odd (see above), it means that x is odd.\r\n" );
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document.write( "Then 7x is odd, and hence 7x + 2y is odd.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Proved and solved.\r
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