document.write( "Question 1116560: solve by addition method.\r
\n" ); document.write( "\n" ); document.write( "4x+4y=3
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Algebra.Com's Answer #731447 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "2x-8y=-1
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document.write( "4x + 4y =  3     (1)\r\n" );
document.write( "2x - 8y = -1     (2)\r\n" );
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document.write( "Multiply equation (1) by 2 (both sides).  Keep equation (2) as is. You get an equivalent system\r\n" );
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document.write( "8x + 8y =  6     (1')\r\n" );
document.write( "2x - 8y = -1     (2')\r\n" );
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document.write( "Now add equations (1') and (2').  The terms \"8y\" will cancel each other, and you will get a single equation for the unique unknown x:\r\n" );
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document.write( "8x + 2x = 6 + (-1),   or\r\n" );
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document.write( "10x = 5.   It implies  x =  =  = 0.5.\r\n" );
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document.write( "Next substitute the found value of x into equation (1).  You will get\r\n" );
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document.write( "4*0.5 + 4y = 3  ====>  4y = 3 - 4*0.5 = 1  ====>  y =  = 0.25.\r\n" );
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document.write( "Answer.  x = 0.5,  y = 0.25.\r\n" );
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document.write( "Check.   4*0.5 + 4*0.25 = 3     ! Correct !\r\n" );
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document.write( "         2*0.5 - 8*0.25 = -1     ! Correct !\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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