Algebra.Com's Answer #749002 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( " +  =  , (1) \r\n" );
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document.write( "x/2 + y/5 = 5. (2)\r\n" );
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document.write( "This system of equations in non-linear.\r\n" );
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document.write( "To make the solution easier, I will introduce NEW VARIABLES a = , b = . Then the system takes the form\r\n" );
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document.write( "a + b = (3)\r\n" );
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document.write( " +  = 5 (4)\r\n" );
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document.write( "To solve it, first simplify equation (4):\r\n" );
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document.write( " + = 5 ====>  = 5 ====> replace a+b by , based on (3) ====>  = 5 ====> ab =  .\r\n" );
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document.write( "Next, from (3), express b = - a and substitute it into equation ab = . You will get\r\n" );
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document.write( "  = ,\r\n" );
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document.write( " -6a^2 + 5a = 1\r\n" );
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document.write( " 6a^2 - 5a + 1 = 0.\r\n" );
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document.write( "Solve the last quadratic equation using the quadratic formula.\r\n" );
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document.write( "You will get two solutions: a=  and a=  .\r\n" );
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document.write( "Thus, the system (3)-(4) has two solutions:\r\n" );
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document.write( " 1) a= , b= - =  = , \r\n" );
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document.write( "and\r\n" );
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document.write( " 2) a = , b= - =  =  = .\r\n" );
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document.write( "Now you need to return from \"a\" and \"b\" to x and y, via the formulas a = , b = .\r\n" );
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document.write( "By doing so, you get two solutions for the original system:\r\n" );
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document.write( "1) x =  =  = 4; y =  =  = 15.\r\n" );
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document.write( "2) x = =  = 6; y = =  = 10.\r\n" );
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document.write( "Answer. The system has two solutions 1) x= 4; y= 15 and 2) x= 6, y= 10.\r\n" );
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document.write( "Solved.\r
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document.write( "You may check that the solution is correct by substituting the found values into the original equations.\r
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document.write( "I am very glad that the tutor @MathLover1 placed her solution here.\r
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document.write( "Comparing these two, you can see how many tons of calculations I saved you from, using my substitutions ! ! ! \r
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document.write( "==============\r
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document.write( "To see other similar solved problems for systems of two non-linear equations in two unknowns, look into the lessons\r
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document.write( " - Solving systems of non-linear equations by reducing to linear ones \r
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document.write( " - Solving systems of non-linear equations in two unknowns using the Cramer's rule \r
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document.write( "in this site.\r
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