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if you have an equation were 5x+3Y=9 would it be correct to say that the independent variable is x because the equation does not solve for..

Mathematics
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Realistically either variable could be considered the independent variable, and the other would be dependent. Traditionally X is the independent variable in math classes, but that's really just an arbitrary choice when faced with a simple equation. If the equation is written as Y= or as X= then you'd typically refer to that variable as the dependent one. The terms really have more meaning in larger problems where you are in fact solving for one variable to determine how it is affected by another. In your example, you could go either way.
Realistically either variable could be considered the independent variable, and the other would be dependent. Traditionally X is the independent variable in math classes, but that's really just an arbitrary choice when faced with a simple equation. If the equation is written as Y= or as X= then you'd typically refer to that variable as the dependent one. The terms really have more meaning in larger problems where you are in fact solving for one variable to determine how it is affected by another. In your example, you could go either way.
Realistically either variable could be considered the independent variable, and the other would be dependent. Traditionally X is the independent variable in math classes, but that's really just an arbitrary choice when faced with a simple equation. If the equation is written as Y= or as X= then you'd typically refer to that variable as the dependent one. The terms really have more meaning in larger problems where you are in fact solving for one variable to determine how it is affected by another. In your example, you could go either way.

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Other answers:

This is a bit overkill wouldn't you sayFreeMathHelp.com? I'd say, the first was a perfect explanation :)
it depends on which variable represents output and which variable represents input the output will always be dependent on the independent variable

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