document.write( "Question 321428: Hi: I wondered if you could check this problem for me... \r \n" );
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document.write( "Solve each system by the addition method. 1/3x -1/6y = 1/3 1/6x+1/4y = 0\r \n" );
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document.write( "This is what I've got, but I'm not sure it's correct... \r \n" );
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document.write( "I started by multiplying both equations by their LCD to get rid of all the fractions. \r \n" );
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document.write( "1/3x – 1/6y = 1/3 \n" );
document.write( "(6)1/3x – (6)1/6y = (6) 1/3 \n" );
document.write( "2x-1y=2\r \n" );
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document.write( "So our first equation is 2x-1y=2\r \n" );
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document.write( "I simplified the second equation by multiplying it by 12:\r \n" );
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document.write( "1/6x+1/4y=0 \n" );
document.write( "(12)1/6x+(12)1/4y=(12)0 \n" );
document.write( "2x+3y=0\r \n" );
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document.write( "The second equation is 2x+3y=0\r \n" );
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document.write( "Now our two equations are:\r \n" );
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document.write( "2x-1y=2 \n" );
document.write( "2x+3y=2\r \n" );
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document.write( "I multiplied the second equation by -1 to eliminate one of the variables:\r \n" );
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document.write( "(-1)2x+(-1)3y=(-1)0 \n" );
document.write( "-2x-3y=0\r \n" );
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document.write( "Added the two equations together and solved:\r \n" );
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document.write( "2x-1y=2 \n" );
document.write( "-2x-3y=0 \n" );
document.write( "-4y= 2 \n" );
document.write( "-4 -4 Reduce the fraction\r \n" );
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document.write( "y= -1/2\r \n" );
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document.write( "Let’s plug this value for y (-1/2) back into the second original equation:\r \n" );
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document.write( "1/6x+1/4(-1/2)=0 \n" );
document.write( "1/6x-1/8=0 Let’s multiply this equation by 24 (the LCD) to get rid of fractions\r \n" );
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document.write( "(24)1/6x-(24)1/8=(24)0 \n" );
document.write( "4x-3=0 \n" );
document.write( " +3 +3 \n" );
document.write( "4x= 3 \n" );
document.write( " 4 4\r \n" );
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document.write( "x= ¾\r \n" );
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document.write( "So, the final solution is (3/4,-1/2)\r \n" );
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document.write( "Because this system only had one solution, this line is independent.\r \n" );
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document.write( "Thanks in advance for your help.\r \n" );
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