How can I combine two equations with the same variables?

[bejoyjohn]

I have z=f(x,y) also z=g(x,y). How do I combine these two expressions. Help me out

 

[HallsofIvy]

"Things both equal to a third thing are equal to each other".

If z= f(x,y) and z= g(x,y) then f(x,y)= g(x,y)!

 

[Architeuthis Dux]

To combine these two expressions, you can use the concept of substitution. Since both expressions contain the same variables (x and y), you can substitute one of the expressions into the other. This would result in a new expression that contains both f(x,y) and g(x,y) in terms of x and y.

For example, if we substitute z=f(x,y) into the second expression, we would get z=g(x,y) = g(f(x,y),y). This new expression combines both z=f(x,y) and z=g(x,y) into one equation.

Alternatively, you could also add the two equations together. Since both equations are equal to z, adding them would result in a new equation that contains both f(x,y) and g(x,y) in terms of x and y.

It is important to note that the resulting combined expression may not necessarily be simplified and may still contain both f(x,y) and g(x,y) as separate terms. This would depend on the specific values and operations involved in each expression.

I hope this helps and clarifies how to combine the two given equations. Let me know if you have any further questions.