document.write( "Question 1030412: (1) ax + by = c
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\n" ); document.write( "\n" ); document.write( "Ralph is trying to solve the system of equations. He begins by subtracting Ax from both sides of equation (1), and then he divides the equation by B. Before he can continue, his friend Alice comes along and says, \"No, you should have subtracted By from both sides, and then divided by A. You will get the wrong answer. Thanks! \n" ); document.write( "
Algebra.Com's Answer #645277 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
(1) ax + by = c
\n" ); document.write( "(2) dx + ey = f\r
\n" ); document.write( "\n" ); document.write( "Ralph is trying to solve the system of equations. He begins
\n" ); document.write( "by subtracting ax from both sides of equation (1),
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\r\n" );
document.write( "Ralph does this:\r\n" );
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document.write( "(1)   ax + by = c\r\n" );
document.write( "     -ax         -ax\r\n" );
document.write( "     ---------------\r\n" );
document.write( "           by = c-ax\r\n" );
document.write( "

\n" ); document.write( "and then he divides the equation by b.
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document.write( "So he does this:\r\n" );
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document.write( "         \"by%2Fb=%28c-ax%29%2Fb\"\r\n" );
document.write( "          \"y=%28c-ax%29%2Fb\" \r\n" );
document.write( "

\n" ); document.write( "Before he can continue, his friend Alice comes along
\n" ); document.write( "and says, \"No, you should have subtracted By from both
\n" ); document.write( "sides, and then divided by A. You will get the wrong answer.
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\r\n" );
document.write( "She is wrong to tell him that he will get the wrong answer, \r\n" );
document.write( "because he will get the right answer if he substitutes \r\n" );
document.write( "\"%28c-ax%29%2Fb\" for y in equation (2) like this:\r\n" );
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document.write( "\"dx+%2B+ey+=+f\"\r\n" );
document.write( "\"dx+%2B+e%28%28c-ax%29%2Fb%29=f\"\r\n" );
document.write( "\"dx+%2Be%28c-ax%29%2Fb=f\"\r\n" );
document.write( "Then multiply by LCD of b\r\n" );
document.write( "\"bdx%2Be%28c-ax%29=bf\"\r\n" );
document.write( "\"bdx%2Bec-eax=bf\"\r\n" );
document.write( "Get terms in x on the left:\r\n" );
document.write( "\"bdx-eax=bf-ec\"\r\n" );
document.write( "Factor out x on the left:\r\n" );
document.write( "\"x%28bd-ea%29=bf-ec\"\r\n" );
document.write( "Divide both sides by (bd-ea)\r\n" );
document.write( "\"x%28bd-ea%29%2F%28bd-ea%29=%28bf-ec%29%2F%28bd-ea%29\"\r\n" );
document.write( "\"x=%28bf-ec%29%2F%28bd-ea%29\"\r\n" );
document.write( "\r\n" );
document.write( "Now although Alice was wrong to tell Ralph that\r\n" );
document.write( "he would get the the wrong answer, the way she\r\n" );
document.write( "said to do it would have been just as good. She \r\n" );
document.write( "would have gotten the same answer as Ralph. She \r\n" );
document.write( "would have found x first and y second, whereas\r\n" );
document.write( "Ralph found y first and x second.\r\n" );
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document.write( "Edwin
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