z=42
x=(y+z)/x
xy+x+y=z
(42-x)/(x+1)=y
x^2-y=42 - solve for z = 42; isolate and then substitute into original equation, assuming it's the same X,Y,Z.
xy+x+y=x^2-y - You can safely cancel out the single Y's.
xy+x=x^2 - Plug in Y's equation that we did from my first post.
x(42-x)/(x+1)+x=x^2 - Multiply the X into the fraction
(42x-x^2)/(x+1)+x=x^2 - Multiply the denominator to all
(42x-x^2)+(x^2+x)=x^3+x^2 - Simplify
43x=x^3+x^2 - Divide by X
43=x^2+x - Change this into a quadratic using "Complete The Squares" method
x^2+x+1/4=43-1/4 - This is result of CTS
(x+1/2)^2=42.75 - Further simplifying
x+0.5=42.75 - Solve for X
x=42.25 or 42 1/4 or 169/4
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Plug x into one of the equations from the list, for this I use the simplest one.
x=(y+z)/x - Isolate the Y
x^2-z=y
(42.25)(42.25)-42=y
1743.0625=y - Used a calculator for final part.
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EDIT: Now we test our values to see if they're correct.
x=(y+z)/x
z=42
x=42.25
y=1743.0625
42.25=(1743.0625+42)/42.25
1785.0625=1785.0625
If, and only if, you plug this into the FIRST equation (since we used second equation to get values, your answer is correct), the values will be incorrect, so these two equations should never mingle in the first place.
