document.write( "Question 54436: I need help. Solve the following system by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent.
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Algebra.Com's Answer #36685 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

I need help. Solve the following system by using\r\n" );
document.write( "either addition or substitution. If a unique \r\n" );
document.write( "solution does not exist, state whether the system \r\n" );
document.write( "is dependent or inconsistent.\r\n" );
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document.write( "By substitution\r\n" );
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document.write( "       10x + 2y = 7 \r\n" );
document.write( "              y = -5x + 3\r\n" );
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document.write( "The second equation is already solved for y.  So replace y\r\n" );
document.write( "in the first equation by (-5x + 3)\r\n" );
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document.write( "        10x + 2y = 7\r\n" );
document.write( "10x + 2(-5x + 3) = 7\r\n" );
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document.write( "Solve that for x if possible\r\n" );
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document.write( "10x + 2(-5x + 3) = 7\r\n" );
document.write( "   10x - 10x + 9 = 7\r\n" );
document.write( "               9 = 7\r\n" );
document.write( "             \r\n" );
document.write( "Oh, oh! The unknowns cancelled out\r\n" );
document.write( "and only a false numerical equation\r\n" );
document.write( "9 = 7 resulted.  So there can be no\r\n" );
document.write( "solution.  This is called an\r\n" );
document.write( "inconsistent system. It has no\r\n" );
document.write( "solution.\r\n" );
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document.write( "[If it had come out a true numerical \r\n" );
document.write( "equation, such as 9 = 9 or 7 = 7, \r\n" );
document.write( "then it would have been a dependent \r\n" );
document.write( "system].\r\n" );
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document.write( "Edwin

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