document.write( "Question 633290: Find the value of a and b so that the solution set is (10,11) \r
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Algebra.Com's Answer #398810 by Edwin McCravy(20056) $\"\"$ $\"About$

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Find the value of a and b so that the solution set is (10,11) \r
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document.write( "You didn't give the system of equations, so I will make up two \r\n" );
document.write( "equations.  Suppose the system of equations were, say this:\r\n" );
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document.write( "ax + by = 53\r\n" );
document.write( "ax - by = -13\r\n" );
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document.write( "Then we substitute x=10 and y=11 into those:\r\n" );
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document.write( "a(10) + b(11) = 53\r\n" );
document.write( "a(10) - b(11) = -13\r\n" );
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document.write( "or\r\n" );
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document.write( "10a + 11b =  53\r\n" );
document.write( "10a - 11b = -13\r\n" );
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document.write( "We add those two equations term by term and get\r\n" );
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document.write( "20a       =  40\r\n" );
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document.write( "          a = 2\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "  10a - 11b = -13\r\n" );
document.write( "10(2) - 11b = -13\r\n" );
document.write( "   20 - 11b = -13\r\n" );
document.write( "       -11b = -33\r\n" );
document.write( "          b = 3\r\n" );
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document.write( "So if a = 2 and b = 3, then the system\r\n" );
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document.write( "ax + by = 53\r\n" );
document.write( "ax - by = -13\r\n" );
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document.write( "will become\r\n" );
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document.write( "2x + 3y = 53\r\n" );
document.write( "2x - 3y = -13\r\n" );
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document.write( "Checking to see:\r\n" );
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document.write( "Adding the two equations term by term gives:\r\n" );
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document.write( "4x     = 40\r\n" );
document.write( "     x = 10\r\n" );
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document.write( "Substitute into\r\n" );
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document.write( "   2x - 3y = -13\r\n" );
document.write( "2(10) - 3y = -13      \r\n" );
document.write( "   20 - 3y = -13\r\n" );
document.write( "       -3y = -33\r\n" );
document.write( "         y = 11\r\n" );
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document.write( "So a=2 and b=3 checks.\r\n" );
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document.write( "Edwin

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