document.write( "Question 572051: 10.81=(10•x)+(12•y)\r
\n" ); document.write( "\n" ); document.write( "Solve.for x and solve for y\r
\n" ); document.write( "\n" ); document.write( "Thanks for your time \n" ); document.write( "
Algebra.Com's Answer #368276 by Theo(13342)\"\" \"About 
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10x + 12y = 10.81
\n" ); document.write( "subtract 10x from both sides of the equation to get:
\n" ); document.write( "12y = 10.81 - 10x
\n" ); document.write( "divide both sides of the equation by 12 to get:
\n" ); document.write( "y = (10.81 - 10x) / 12
\n" ); document.write( "go back to your original equation.
\n" ); document.write( "10x + 12y = 10.81
\n" ); document.write( "subtract 12y from both sides of the equation to get:
\n" ); document.write( "10x = 10.81 - 12y
\n" ); document.write( "divide both sides of the equation by 10 to get:
\n" ); document.write( "x = (10.81 - 12y) /10
\n" ); document.write( "those are your answers.
\n" ); document.write( "you can solve y in terms of x or your can solve for x in terms of y, but you can't solve for both with only one equation.
\n" ); document.write( "generally speaking, you need the same number of equations as the number of unknowns in order to get a single solution for each unknown.
\n" ); document.write( "if you tried to use the value for y that you got in the same equation to solve for x, you would end up with an identity as shown below:
\n" ); document.write( "your original equation is:
\n" ); document.write( "10x + 12y = 10.81
\n" ); document.write( "you solve for y in terms of x to get:
\n" ); document.write( "y = (10.81 - 10x) / 12
\n" ); document.write( "you substitute for y in the original equation to get:
\n" ); document.write( "10x + 12((10.81 - 10x) / 12) = 10.81
\n" ); document.write( "simplify this to get:
\n" ); document.write( "10x + 10.81 - 10x = 10.81
\n" ); document.write( "subtract 10.81 from both sides of this equation to get:
\n" ); document.write( "10x - 10x = 10.81 - 10.81
\n" ); document.write( "simplify to get:
\n" ); document.write( "0 = 0
\n" ); document.write( "that's an identity equation.
\n" ); document.write( "there are no variables in it and the equation is true because 0 really does equal to 0.
\n" ); document.write( "what this means is that x and y can be any value and this equation will always be true.
\n" ); document.write( "you did not narrow down the result to one value for x and one value for y because that's impossible to do with 2 unknowns and only 1 equation.
\n" ); document.write( "the best you can do, as stated above, is narrow the solution down to 1 unknown in terms of the other unknown.
\n" ); document.write( "now, when you assume a value for the other unknown, you can get a single solution for the one unknown.
\n" ); document.write( "the solution of:
\n" ); document.write( "y = (10.81 - 10x) / 12
\n" ); document.write( "will narrow down to one solution if you assume a value for x.
\n" ); document.write( "example:
\n" ); document.write( "assume x = 1.081
\n" ); document.write( "the equation will then become:
\n" ); document.write( "y = (10.81 - 10*1.081) / 12 which becomes:
\n" ); document.write( "y = (10.81 - 10.81) / 12 which becomes:
\n" ); document.write( "y = 0 / 12 which becomes:
\n" ); document.write( "y = 0.
\n" ); document.write( "when x = 1.081, y = 0
\n" ); document.write( "go back to your original equation of:
\n" ); document.write( "10x + 12y = 10.81
\n" ); document.write( "replace x with 1.081 and replace 6 with 0 to get:
\n" ); document.write( "10(1.081) + 12(0) = 10.81
\n" ); document.write( "simplify to get:
\n" ); document.write( "10.81 = 10.81
\n" ); document.write( "since this is a true equation (10.81 really does equal to 10.81), the values for x and y are good.\r
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