document.write( "Question 1062359: The system of equations I need to solve is:
\n" ); document.write( "7x - 8y = 24
\n" ); document.write( "xy^2 = 1\r
\n" ); document.write( "\n" ); document.write( "In the second, it's not (xy)^2, but just the y is squared. I get to substitution and replace y in the second equation with y = (7/8)x + 3 and end up with (23/32)x^3 + (21/4)x^2 + 9x - 1 = 0. My professor warned that this problem is pure evil and said at this point I would need to use rational root theorem and that there IS a rational root. Issue is I don't know how to find a rational root from a fraction as a leading coefficient (23/32).... Unless I screwed up before that and that's not what I'm looking at. \r
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Algebra.Com's Answer #677260 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!
The system of equations I need to solve is:
\n" ); document.write( "7x - 8y = 24
\n" ); document.write( "xy^2 = 1\r
\n" ); document.write( "\n" ); document.write( "In the second, it's not (xy)^2, but just the y is squared. I get to substitution and replace y in the second equation with y = (7/8)x + 3 and end up with (23/32)x^3 + (21/4)x^2 + 9x - 1 = 0. My professor warned that this problem is pure evil and said at this point I would need to use rational root theorem and that there IS a rational root. Issue is I don't know how to find a rational root from a fraction as a leading coefficient (23/32).... Unless I screwed up before that and that's not what I'm looking at. \r
\n" ); document.write( "\n" ); document.write( "Any help to get me beyond this point will be greatly appreciated.
\n" ); document.write( "

It's not that bad as your professor professed.
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document.write( " ------- eq (ii) ==========> You got up to this point
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document.write( "You have: , but it should be: 
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document.write( " ----- Substituting  for y in eq (ii)
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document.write( " ----- FOILing 	
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document.write( " ---- Multiplying TRINOMIAL in parentheses by LCD, 64
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document.write( " ------ Cross-multiplying
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document.write( " ------- Distributing left-side
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document.write( " ---- Subtracting 64 from each side
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document.write( "Now is the time you use the rational root theorem with factors of 49 or 64. You will find that 4 is a root, so: x = 4, and x - 4 is a factor.\r
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document.write( "Using the factor x - 4, and SYNTHETIC DIVISION or LONG DIVISION of POLYNOMIALS, you will find that the QUOTIENT when  is divided by x - 4 is: . 
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document.write( "Therefore, the factors of  are . 
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document.write( "You just need to use the quadratic equation formula or COMPLETING THE SQUARE to get the final 2 factors of , which happen to be REAL also (2.73787877 and 0.1193).
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document.write( "You have 3 values for x, so substitute each one into the SIMPLER original equation [eq (i) or (ii)] to find each CORRESPONDING y-value. \r
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document.write( "That's it!! The trick here is to do things in STEPS, or LITTLE by LITTLE. That way, you won't be confused and make mistakes. \n" );
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