document.write( "Question 1035244: Solve the following equation for x and y:
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Algebra.Com's Answer #649896 by ikleyn(52797) $\"\"$ $\"About$

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document.write( "Since you do not use parentheses properly, there are several ways to read your system.\r\n" );
document.write( "Your writing is ambiguous. To avoid ambiguity, use parentheses.\r\n" );
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document.write( "Is THIS modification what you want?\r\n" );
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document.write( " = ,     (1)\r\n" );
document.write( " = .     (2)\r\n" );
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document.write( "Below is the solution of this system.\r\n" );
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document.write( "Since  = ,  = ,  = ,  = , you can rewrite the system (1), (2) in the form\r\n" );
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document.write( " +  = ,      (1')\r\n" );
document.write( " +  = .       (2')\r\n" );
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document.write( "This system is still non-linear.\r\n" );
document.write( "The way to solve it is to introduce new variables u =  and v = .\r\n" );
document.write( "Then the system (1'), (2') takes the form\r\n" );
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document.write( "4u + 27v = 275,         (3)\r\n" );
document.write( "8u +  9v = 145.         (4)\r\n" );
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document.write( "The system (3), (4) is just a linear, and we can easily solve it.\r\n" );
document.write( "I will use the Elimination method. Multiply equation (3) by 2 (both sides). You will get\r\n" );
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document.write( "8u + 54v = 550,         (3')\r\n" );
document.write( "8u +  9v = 145.         (4')\r\n" );
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document.write( "Now, distract (3') from (4'). You will get\r\n" );
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document.write( "54v - 9v = 550 - 145  --->  45v = 405  --->  v =  = 9.\r\n" );
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document.write( "Now recall that v = ,  or  9 = .  Hence,  y = 2,  and one unknown is just found.\r\n" );
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document.write( "Next, from (3)  u =  =  =  = 8.\r\n" );
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document.write( "Again, recall that  u = ,  or 8 = .  Hence,  x = 3.\r\n" );
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document.write( "The problem is solved.\r\n" );
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document.write( "Answer.  x = 3,  y = 2.\r\n" );
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document.write( "You can check that the solution is correct.\r\n" );
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