document.write( "Question 459301: How do I Determine whether the two lines are parallel, perpendicular, or neither parallel nor perpendicular. Do I add the like terms together?\r
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\n" ); document.write( "9x + 3y = 15 \n" ); document.write( "

Algebra.Com's Answer #314977 by Edwin McCravy(20060) $\"\"$ $\"About$

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How do I Determine whether the two lines are parallel, perpendicular, or neither parallel nor perpendicular. Do I add the like terms together?
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document.write( "12x + 4y = 16\r\n" );
document.write( " 9x + 3y = 15\r\n" );
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document.write( "You don't add the like terms together until\r\n" );
document.write( "you have multiplied them through by whatever\r\n" );
document.write( "you need to multiply them by so that when you\r\n" );
document.write( "add the like terms together, one of the letters\r\n" );
document.write( "x or y, will cancel out.\r\n" );
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document.write( "To make the y terms cancel out:\r\n" );
document.write( "1.  Find the least common multiple of the coefficients\r\n" );
document.write( "    of y.  They are 4 and 3 and their least common\r\n" );
document.write( "    multiple is 4×3 or 12.\r\n" );
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document.write( "2. Multiply the first equation though by 3 to make the \r\n" );
document.write( "   4y into a 12y, like this:\r\n" );
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document.write( "   36x + 12y = 48\r\n" );
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document.write( "3. Multiply the second equation through by -4 to make \r\n" );
document.write( "   the 3y into a -12y so it will cancel with the 12y\r\n" );
document.write( "   when we add like terms:\r\n" );
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document.write( "   9x +  3y =  15\r\n" );
document.write( " -36x - 12y = -60 \r\n" );
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document.write( "4. Add the like terms:\r\n" );
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document.write( "   36x + 12y =  48\r\n" );
document.write( "  -36x - 12y = -60\r\n" );
document.write( "------------------\r\n" );
document.write( "    0x +  0y = -12\r\n" );
document.write( "           0 = -12\r\n" );
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document.write( "That is false so the system is inconsistent and there\r\n" );
document.write( "are no solutions. So the lines do not cross so they\r\n" );
document.write( "are parallel.  \r\n" );
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document.write( "Edwin

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