document.write( "Question 116495: This question is about augmented matrices. The question says: Set up and solve the following systems of equations using augmented matrices,\r
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\n" ); document.write( "6x-4y=1 What are the X and Y values? \n" ); document.write( "

Algebra.Com's Answer #84744 by Edwin McCravy(20063) $\"\"$ $\"About$

You can put this solution on YOUR website!
This question is about augmented matrices. The question says: Set up and solve the following systems of equations using augmented matrices,
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document.write( "Abbreviate\r\n" );
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document.write( "3x - 2y = 8\r\n" );
document.write( "6x - 4y = 1\r\n" );
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document.write( "by the augmented matrix:\r\n" );
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document.write( "[3 -2 | 8]\r\n" );
document.write( "[6 -4 | 1]\r\n" );
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document.write( "The idea is to use row operations to get 0's\r\n" );
document.write( "where the 6 and the -2 are, and then to get\r\n" );
document.write( "1's where the 3 and -4 are.\r\n" );
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document.write( "First let's get a 0 where the 6 is:\r\n" );
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document.write( "Multiply the top row by -2 and the bottom\r\n" );
document.write( "row by 1:\r\n" );
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document.write( "[-6  4 | -16]\r\n" );
document.write( "[ 6 -4 |   1]\r\n" );
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document.write( "Now add the top row to the bottom row:\r\n" );
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document.write( "[-6  4 | -16]\r\n" );
document.write( "[ 0  0 | -15]\r\n" );
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document.write( "Oh oh!  There is no way to get a 0 where \r\n" );
document.write( "the 4 is.  So we get a 1 where the -6 is by\r\n" );
document.write( "dividing the top row through by -6\r\n" );
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document.write( "[-6/-6  4/-6 | -16/-6]\r\n" );
document.write( "[    0     0 |    -15]\r\n" );
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document.write( "or\r\n" );
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document.write( "[ 1 -2/3 | 8/3]\r\n" );
document.write( "[ 0    0 | -15]\r\n" );
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document.write( "Now write this matrix as the system of which\r\n" );
document.write( "it is an abbreviation:\r\n" );
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document.write( " 1x - (2/3)y = 8/3 \r\n" );
document.write( " 0x +     0y = -15\r\n" );
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document.write( "But the bottom equation says 0 = -15 which\r\n" );
document.write( "is false and therefore there is no solution.\r\n" );
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document.write( "Such a system is called \"inconsistent\" which\r\n" );
document.write( "means if you tried to solve them graphically\r\n" );
document.write( "you would get two parallel lines which will\r\n" );
document.write( "never intersect.\r\n" );
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document.write( "Here is the graph of the two lines where you\r\n" );
document.write( "can see they are parallel:\r\n" );
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document.write( "3x - 2y = 8\r\n" );
document.write( "6x - 4y = 1\r\n" );
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document.write( "Edwin

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