document.write( "Question 428471: I need to use substitution method
\n" ); document.write( "15x-10y=1
\n" ); document.write( "5y=-2+15x \n" ); document.write( "

Algebra.Com's Answer #853236 by ikleyn(53419) $\"\"$ $\"About$

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\n" ); document.write( "I need to use substitution method
\n" ); document.write( "15x - 10y = 1
\n" ); document.write( "5y = -2 + 15x
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\n" ); document.write( "\n" ); document.write( " It can be solved in much more efficient way than @mananth does it in his post.\r
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\n" ); document.write( "\n" ); document.write( " I will apply a \" smart \" substitution method.\r
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document.write( "Your starting equations are \r\n" );
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document.write( "    15x - 10y = 1    (1)\r\n" );
document.write( "    5y = -2 + 15x    (2)\r\n" );
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document.write( "From equation (2), express  15x = 5y + 2 and substitute it as a whole block into equation (1), \r\n" );
document.write( "replacing the term 15x there\r\n" );
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document.write( "    (5y + 2) - 10y = 1,\r\n" );
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document.write( "     5y - 10y = 1 - 2,\r\n" );
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document.write( "        -5y   =   -1\r\n" );
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document.write( "          y   =   1/5 = 0.2.\r\n" );
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document.write( "Now substitute y = 0.2 into equation (1) and find x\r\n" );
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document.write( "    15x - 10*0.2 = 1,\r\n" );
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document.write( "    15x - 2 = 1,\r\n" );
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document.write( "    15x = 1 + 2 = 3,\r\n" );
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document.write( "      x = 3/15 = 0.2.\r\n" );
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document.write( "ANSWER.  x = 0.2,  y = 0.2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "As you see, in this case \" smart \" substitution works more effectively
\n" ); document.write( "than a standard \" stupid \" substitution.\r
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\n" ); document.write( "\n" ); document.write( "The meaning of this problem for you is to learn advantages of \"smart\" substitution method.\r
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