document.write( "Question 1116568: solve by addition method.\r
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Algebra.Com's Answer #731453 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( " 8x - 3y =  18     (1)\r\n" );
document.write( " 4x + 5y =  -4     (2)\r\n" );
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document.write( "Multiply equation (2) by (-2) (both sides).  Keep equation (1) as is. You get an equivalent system\r\n" );
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document.write( " 8x -  3y = 18     (1')\r\n" );
document.write( "-8x - 10y =  8     (2')\r\n" );
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document.write( "Now add equations (1') and (2').  The terms \"8x\" will cancel each other, and you will get a single equation for the unique unknown y:\r\n" );
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document.write( "-3y + (-10y) = 18 + 8,   or\r\n" );
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document.write( "-13y = 26.   It implies  y =  = -2.\r\n" );
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document.write( "Next substitute the found value of y into equation (1).  You will get\r\n" );
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document.write( "8x - 3*(-2) = 18  ====>  8x = 18 + 3*(-2) = 12  ====>  x =  = .\r\n" );
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document.write( "Answer.  x = ,  y = -2.\r\n" );
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document.write( "Check the answer on your own.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice that the standard and official name of this method is \"the Elimination method\".\r
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\n" ); document.write( "\n" ); document.write( "On solving systems of linear equations in two unknowns see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns by the Substitution method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns by the Elimination method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns using determinant \r
\n" ); document.write( "\n" ); document.write( "    - Geometric interpretation of a linear system of two equations in two unknowns \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Systems of two linear equations in two unknowns\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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