SOLUTION: 10.81=(10�x)+(12�y) Solve.for x and solve for y Thanks for your time

Question 572051: 10.81=(10�x)+(12�y)
Solve.for x and solve for y
Thanks for your time
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
10x + 12y = 10.81
subtract 10x from both sides of the equation to get:
12y = 10.81 - 10x
divide both sides of the equation by 12 to get:
y = (10.81 - 10x) / 12
go back to your original equation.
10x + 12y = 10.81
subtract 12y from both sides of the equation to get:
10x = 10.81 - 12y
divide both sides of the equation by 10 to get:
x = (10.81 - 12y) /10
those are your answers.
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.
generally speaking, you need the same number of equations as the number of unknowns in order to get a single solution for each unknown.
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:
your original equation is:
10x + 12y = 10.81
you solve for y in terms of x to get:
y = (10.81 - 10x) / 12
you substitute for y in the original equation to get:
10x + 12((10.81 - 10x) / 12) = 10.81
simplify this to get:
10x + 10.81 - 10x = 10.81
subtract 10.81 from both sides of this equation to get:
10x - 10x = 10.81 - 10.81
simplify to get:
0 = 0
that's an identity equation.
there are no variables in it and the equation is true because 0 really does equal to 0.
what this means is that x and y can be any value and this equation will always be true.
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.
the best you can do, as stated above, is narrow the solution down to 1 unknown in terms of the other unknown.
now, when you assume a value for the other unknown, you can get a single solution for the one unknown.
the solution of:
y = (10.81 - 10x) / 12
will narrow down to one solution if you assume a value for x.
example:
assume x = 1.081
the equation will then become:
y = (10.81 - 10*1.081) / 12 which becomes:
y = (10.81 - 10.81) / 12 which becomes:
y = 0 / 12 which becomes:
y = 0.
when x = 1.081, y = 0
go back to your original equation of:
10x + 12y = 10.81
replace x with 1.081 and replace 6 with 0 to get:
10(1.081) + 12(0) = 10.81
simplify to get:
10.81 = 10.81
since this is a true equation (10.81 really does equal to 10.81), the values for x and y are good.

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