document.write( "Question 1036350: Solve for x and y
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Algebra.Com's Answer #651064 by ikleyn(52781) $\"\"$ $\"About$

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Solve for x and y
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document.write( " = ,    (1)\r\n" );
document.write( " = .   (2)\r\n" );
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document.write( "The standard way to solve problems like this, is to introduce new variables\r\n" );
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document.write( "u = ,    (3)\r\n" );
document.write( "v = .    (4)\r\n" );
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document.write( "Then the system of non-linear equations (1) and (2) becomes the system of linear equations\r\n" );
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document.write( "15u + 22v =  5,    (5)\r\n" );
document.write( "40u + 55v = 13.    (6)\r\n" );
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document.write( "To solve it, apply the Elimination method. Multiply equation (5) by 8 (both sides) and multiply the equation (6) by 3, \r\n" );
document.write( "then distract. You will get\r\n" );
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document.write( "176v - 165v = 40 - 39   --->  11v = 1   --->  v = .\r\n" );
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document.write( "Now, from (5)  \r\n" );
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document.write( "15u = 5 - 22v =   --->   15u = 3   --->   u =  = .\r\n" );
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document.write( "Returning back to the original unknowns x and y, you have\r\n" );
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document.write( "x - y =  5,    (7)\r\n" );
document.write( "x + y = 11.    (8)\r\n" );
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document.write( "Now we are at the finish line. Add (7) and (8), and you will get\r\n" );
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document.write( "2x = 16   --->  x =  = 8. \r\n" );
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document.write( "From (8),  y = 11 - x = 11 - 8 = 3.\r\n" );
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document.write( "Answer. x = 8, y = 3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn is the method of introducing these new variables.\r
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