document.write( "Question 1030611: Solve the system of equations by using substitution. Express the answer as an ordered pair:
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Algebra.Com's Answer #853866 by ikleyn(53742) $\"\"$ $\"About$

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\n" ); document.write( "Solve the system of equations by using substitution. Express the answer as an ordered pair:
\n" ); document.write( " x - 5y = 2
\n" ); document.write( "9x + 8 = 15y
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\n" ); document.write( "\n" ); document.write( "Solving systems of linear equations is an algorithmic procedure, from one side,
\n" ); document.write( "and an art, from the other side - both at the same time. Teaching students to solve
\n" ); document.write( "such systems is teaching to algorithmic procedure and teaching to the art, in the same time.\r
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\n" ); document.write( "\n" ); document.write( "In the given system, the coefficient at 'x' in the first equation equals 1, so it is very natural
\n" ); document.write( "to express 'x' from this equation and to substitute this expression into the second equation.\r
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\n" ); document.write( "\n" ); document.write( "@mananth uses his computer code, which is written in stiff manner and knows nothing about the art of solving.
\n" ); document.write( "It only performs one preassigned/programmed procedure, which is not appropriate for this given system of
\n" ); document.write( "equations. Therefore, the @mananth' solution is absolutely inappropriate for solving this concrete system
\n" ); document.write( "and is inappropriate in degree 2 for TEACHING students on solving this system and other similar systems.\r
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document.write( "Your starting equations are \r\n" );
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document.write( "     x - 5y = 2        (1)\r\n" );
document.write( "    9x + 8  = 15y      (2)\r\n" );
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document.write( "From the first equation, express\r\n" );
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document.write( "    x = 5y + 2         (3)\r\n" );
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document.write( "and substitute it into the second equation\r\n" );
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document.write( "    9(5y+2) + 8 = 15y.\r\n" );
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document.write( "Now simplify it and find y\r\n" );
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document.write( "    45y + 18 + 8 = 15y,\r\n" );
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document.write( "    45y - 15y = - 26,\r\n" );
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document.write( "       30y    = -26,\r\n" );
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document.write( "         y =  = .\r\n" );
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document.write( "Now substitute this value of 'y'  into (3) and find 'x'\r\n" );
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document.write( "    x =  =  =  = .\r\n" );
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document.write( "ANSWER.  The solution of the system is  x = ,  y = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "The final answer in the post by @mananth is $\"highlight%28highlight%28INCORRECT%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Again, the way on how @mananth solves this system, is inappropriate.\r
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\n" ); document.write( "\n" ); document.write( "His computer code is written in stiff manner; it is not able to adapt to the form of equations
\n" ); document.write( "and to find an optimal way of solution. In this form and due to this reason, his code
\n" ); document.write( "is inappropriate for using in teaching.\r
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