document.write( "Question 1023531: please help answer this systems of equations: substitution and elimination method , please show all work.\r
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Algebra.Com's Answer #639033 by ikleyn(52879) $\"\"$ $\"About$

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\n" ); document.write( "please help answer this systems of equations: substitution and elimination method , please show all work.\r
\n" ); document.write( "\n" ); document.write( "y = -4x-8
\n" ); document.write( "-8x-4y = -8
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\n" ); document.write( "\n" ); document.write( "1. Substitution method\r
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document.write( "y = -4x - 8      (1)\r\n" );
document.write( "-8x - 4y = -8    (2)\r\n" );
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document.write( "You just have y expressed via x in the equation (1).\r\n" );
document.write( "So, simply substitute this expression for y into the equation (2).\r\n" );
document.write( "You will get a single equation for x:\r\n" );
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document.write( "-8x - 4*(-4x - 8) = -8.    (3)\r\n" );
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document.write( "Simplify and solve it:\r\n" );
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document.write( "-8x +16x + 32 = -8,\r\n" );
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document.write( "8x + 32 = -8,\r\n" );
document.write( "8x = -8 - 32,\r\n" );
document.write( "8x = -40,\r\n" );
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document.write( "x =  = .\r\n" );
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document.write( "Then, according to (1), y = -4x - 8 = -4*(-5) - 8 = 20 - 8 = 12.\r\n" );
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document.write( "Answer.  x = -5, y = 12.\r\n" );
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\n" ); document.write( "\n" ); document.write( "2. Elimination method\r
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document.write( "Rewrite your original system in an equivalent form\r\n" );
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document.write( " 4x +  y = -8    (1')\r\n" );
document.write( "-8x - 4y = -8    (2')\r\n" );
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document.write( "Now multiply the equation (1') by 2 and add to the equation (2'). \r\n" );
document.write( "In this way you eliminate the unknown x and get a single equation for the unknown y:\r\n" );
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document.write( "2y - 4y = -16 - 8.\r\n" );
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document.write( "Simplify it:\r\n" );
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document.write( "-2y = -24,\r\n" );
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document.write( "y =  = 12.\r\n" );
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document.write( "Then from (1') 4x = -8 -y = -8 - 12 = -20 and x =  = -5.\r\n" );
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document.write( "Thus you got the same answer.\r\n" );
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