document.write( "Question 1199807: 6x-5y= -30
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Algebra.Com's Answer #833789 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "The starting system of equations is\r\n" );
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document.write( "    6x - 5y = -30     (1)\r\n" );
document.write( "    2x + 2y =  12     (2)\r\n" );
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document.write( "Multiply equation (2) by 3 (both sides). Keep equation (1) as is.  You get\r\n" );
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document.write( "    6x - 5y = -30     (3)\r\n" );
document.write( "    6x + 6y =  36     (4)\r\n" );
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document.write( "Now equations (3) and (4) have the same coefficient at x.\r\n" );
document.write( "Therefore, you subtract equation (3) from equation (4), and you annihilate the terms \"6x\" this way.\r\n" );
document.write( "You get then\r\n" );
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document.write( "         6y - (-5y) = 36 - (-30)\r\n" );
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document.write( "            11y     =    66\r\n" );
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document.write( "              y     =    66/11 = 6.\r\n" );
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document.write( "Then from equation (2)\r\n" );
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document.write( "    2x = 12 - 2y = 12 - 2*6 = 0.\r\n" );
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document.write( "ANSWER.  x = 0, y = 6.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "You may check it that the answer is correct
\n" ); document.write( "by substituting the found values in original equations.\r
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\n" ); document.write( "\n" ); document.write( "It looks like you need to learn (to get familiar with) the general theory/technique on solving systems of two equations in two unknown.\r
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\n" ); document.write( "\n" ); document.write( "In this site I developed such lessons for beginner students. These lessons are\r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Substitution method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Elimination method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns using determinant \r
\n" ); document.write( "\n" ); document.write( "    - Geometric interpretation of the linear system of two equations in two unknowns \r
\n" ); document.write( "\n" ); document.write( "    - Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method \r
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\n" ); document.write( "\n" ); document.write( "They give you the general theory and a lot of examples which you can consider as your TEMPLATES.\r
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\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook, your handbook, your guide and your (free of charge) home teacher.\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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