document.write( "Question 1203089: x*y=2x-y find the value of y if y*(3*y)=6 \n" ); document.write( "
Algebra.Com's Answer #838361 by Theo(13342)\"\" \"About 
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your two equations are:
\n" ); document.write( "x*y=2x-y
\n" ); document.write( "y*(3*y)=6
\n" ); document.write( "simplify to get:
\n" ); document.write( "x*y = 2x - y
\n" ); document.write( "3y^2 = 6
\n" ); document.write( "in the first equation:
\n" ); document.write( "add y to both sides of the equation to get x*y + y = 2x
\n" ); document.write( "factor out the y to get:
\n" ); document.write( "y * (x + 1) = 2x
\n" ); document.write( "solve for y to get:
\n" ); document.write( "y = 2x / (x + 1)
\n" ); document.write( "in the second equation solve for y^2 to get:
\n" ); document.write( "y^2 = 2
\n" ); document.write( "since y = 2x / (x + 1), then:
\n" ); document.write( "y^2 = 4x^2 / (x^2 + 2x + 1)
\n" ); document.write( "your equation of y^2 = 2 becomes:
\n" ); document.write( "4x^2 / (x^2 + 2x + 1) = 2
\n" ); document.write( "multiply both sides of this equation by (x^2 + 2x + 1) to get:
\n" ); document.write( "4x^2 = 2 * (x^2 + 2x + 1)
\n" ); document.write( "simplify to ge:
\n" ); document.write( "4x^2 = 2x^2 + 4x + 2
\n" ); document.write( "subtract the right hand side of the equation from both sides of the equation to get:
\n" ); document.write( "4x^2 - 2x^2 - 4x - 2 = 0
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "2x^2 - 4x - 2 = 0
\n" ); document.write( "factor out a 2 to get:
\n" ); document.write( "x^2 - 2x - 1 = 0
\n" ); document.write( "factor this quadratic equation to get:
\n" ); document.write( "x = 2.4142135623731 or x = -0.4142135623731
\n" ); document.write( "to confirm, replace x with either of these values in the original equation to solve the original problem.
\n" ); document.write( "the original problem gives you the original equation of x*y=2x-y.
\n" ); document.write( "it then asks you to find the value of y if y * (3 * y) = 6
\n" ); document.write( "i think it might be asking you to find the value of x is y * (3 * y) = 6
\n" ); document.write( "i solved for x to get the values of x above.
\n" ); document.write( "i also solved for y in the second equation to get y^2 = 2
\n" ); document.write( "thqat would make y equal to plus or minus sqrt(2).
\n" ); document.write( "using the values of x above, i replaced x in the original equation of x*y = (2x -y,
\n" ); document.write( "solving for y in that equation, i got y = 2x / (x + 1).\r
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\n" ); document.write( "\n" ); document.write( "using the value of x i derived above, i got y = plus or minus sqrt(2).\r
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\n" ); document.write( "\n" ); document.write( "i graphed both equation and got what you see below:\r
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\n" ); document.write( "\n" ); document.write( "\r
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\n" ); document.write( "\n" ); document.write( "your solution is that y = sqrt(2) when x = 2.4142135623731 and y = -sqrt(2) when x = -0.4142135623731.\r
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\n" ); document.write( "\n" ); document.write( "alternatively, your solution is that x = 2.4142135623731 when y = sqrt(2) and x = -0.4142135623731 when y = -sqrt(2).\r
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\n" ); document.write( "\n" ); document.write( "i used a quadratic solver to find the values of x.
\n" ); document.write( "here are the results from that quadratic equation solver.\r
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\n" ); document.write( "\n" ); document.write( "not that y = -1.414 and y 1.414 that you see on the graph is a rounded version of y = -sqrt(2) and y = sqrt(2).\r
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