document.write( "Question 1019997: Use the method of elimination through addition to solve the following system of equations.
\n" ); document.write( "(1) x/2 + y/5 = 1/2
\n" ); document.write( "(2) 3x - y = -8 \n" ); document.write( "

Algebra.Com's Answer #635953 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Use the method of elimination through addition to solve the following system of equations.
\n" ); document.write( "(1) x/2 + y/5 = 1/2
\n" ); document.write( "(2) 3x - y = -8
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document.write( "x/2 + y/5 = 1/2,    (1)\r\n" );
document.write( "3x  - y   = -8.     (2)\r\n" );
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document.write( "Multiply equation (1) by 10 (both sides) to rid off denominators. You will get\r\n" );
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document.write( "5x + 2y = 5         (3)\r\n" );
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document.write( "instead of (1), and it is good. Now you have the system of two equations \r\n" );
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document.write( "5x + 2y =  5,       (3)\r\n" );
document.write( "3x -  y = -8.       (2)\r\n" );
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document.write( "Now multiply equation (2) by 2 (both sides) and then add to equation (3).\r\n" );
document.write( "By doing this, you eliminate the unknown y and get a single equation for the unknown x:\r\n" );
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document.write( "5x + 6x = 5 + 2*(-8),   or\r\n" );
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document.write( "11x = -11.\r\n" );
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document.write( "Hence, x = -1.\r\n" );
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document.write( "Now from (2) you have y = 3x + 8 = 3*(-1) + 8 = 5.\r\n" );
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document.write( "The system is solved. The solution is x = -1, y = 5.\r\n" );
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