document.write( "Question 1190535: I'm having a really hard time understanding solving using elimination. Could somebody explain it to me in lots of detail.
\n" ); document.write( "x-y=3 and 2x+4y=9 \n" ); document.write( "
Algebra.Com's Answer #822211 by ikleyn(52776)\"\" \"About 
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\n" ); document.write( "I'm having a really hard time understanding solving using elimination. Could somebody explain it to me in lots of detail.
\n" ); document.write( "x-y=3 and 2x+4y=9
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\n" ); document.write( "\n" ); document.write( "            Specially for the given problem,  the procedure  (the  Elimination method)  works as follows.\r
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document.write( "Your starting system is\r\n" );
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document.write( "     x -  y = 3     (1)\r\n" );
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document.write( "    2x + 4y = 9     (2)\r\n" );
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document.write( "Now multiply first equation by 2 (both sides). Keep the second equation as is. You will get\r\n" );
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document.write( "    2x - 2y = 6     (3)\r\n" );
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document.write( "    2x + 4y = 9     (4)\r\n" );
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document.write( "Next, subtract equation (3) from equation (4). \r\n" );
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document.write( "The terms \"2x\" in both equations will cancel each other, and you will obtain an equation for one single unknown \"y\":\r\n" );
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document.write( "    4y - (-2y) = 9 - 6,\r\n" );
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document.write( "or\r\n" );
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document.write( "       6y      =   3\r\n" );
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document.write( "        y      =   3/6 = 0.5.\r\n" );
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document.write( "So, one unknown is just found: y = 0.5.\r\n" );
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document.write( "To find another unknown \"x\", substitute the found value y= 0.5 into EITHER equation (1) or (2),\r\n" );
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document.write( "For example, substituting into equation (1) gives you\r\n" );
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document.write( "    x = 3 + y = 3 + 0.5 = 3.5.\r\n" );
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document.write( "At this point, the problem is just solved, and the answer is  x= 3.5,  y= 0.5.\r\n" );
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document.write( "You may check (and you MUST check) the answer by substituting the found values into the original / (given) equations.\r\n" );
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document.write( "I leave this job to you, since it is elementary.\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point,  the solution is complete.\r
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\n" ); document.write( "\n" ); document.write( "The idea of the method is to make the coefficients  EQUAL  in two equations for some
\n" ); document.write( "of the two unknowns,  and then subtract equations,  ELIMINATING  this unknown.\r
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\n" ); document.write( "\n" ); document.write( "Having this explained solution,  please  NEVER  say again that you do not understand the subject:
\n" ); document.write( "it was explained to you in the most comprehensive and detailed way.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems,  look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Elimination method \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 lesson is 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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