document.write( "Question 46342: the sum of two numbers is two hundred thirty. their difference is sixty. what are the numbers? *SOLVE USING A SYSTEM OF EQUATIONS \n" ); document.write( "

Algebra.Com's Answer #30751 by mszlmb(115) $\"\"$ $\"About$

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Let the two numbers be X and Y, X being the larger number if there is one.\r\n" );
document.write( "X+Y=230\r\n" );
document.write( "X-Y=60\r\n" );
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document.write( "Take the second equation:\r\n" );
document.write( "X+Y=30  minus X on both sides\r\n" );
document.write( "Y=230-X\r\n" );
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document.write( "Now solve by substitution:\r\n" );
document.write( "We know Y=230-X from the first problem, so replace Y in the second problem by (230-X)\r\n" );
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document.write( "X-(230-X)=60  distribute the invisible -1\r\n" );
document.write( "X-230+X=60  +230 on both sides\r\n" );
document.write( "2X=290  divide by 2 on both sides\r\n" );
document.write( "X=145\r\n" );
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document.write( "Knowing this, we go back to the second equation to replace X with 145 and get Y:\r\n" );
document.write( "145-Y=60  minus 145 on both sides\r\n" );
document.write( "-Y=-85  times -1 on both sides\r\n" );
document.write( "Y=85\r\n" );
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document.write( "X=145\r\n" );
document.write( "Y=85

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