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In an equation x = y + k

Where: "$x$" is a known variable, "$y$" is an unknown variable and "$k$" is an unknown constant.

How could "$y$" and "$k$" values be calculated?

Is it possible to get exact values?

My initial thinking is that it can't be solved, but since my math knowledge is very basic I'd like some opinions, and of course the reasoning behind.

Thanks in advance.

2 Answers 2

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If $y$ is unknown (and you never know its values), then $k$ cannot be determined, since for any number $c$ you can also write $x = (y-c) + (c+k) = y_c + (c+k)$, where $y_c = y-c$. Here, $y_c$ is another unknown variable and $c+k$ is another unknown constant.

This also means that you can assume that $k=0$, since replacing $y$ with $y_k$ gives the equation $x = y_k$, and so $x$ and $y_k$ are the same. These ideas crop up when you do integrals in calculus --- you don't care about adding a constant on to the end of the function, and so you consider the family of functions of the form $y + c$, where $c$ is any number.

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This equation refers to the family of equation of a linee with slope as unity and varying intercept on the axes.

So, if you look it that way, it becomes very clear that it is impossible to calculate y and k from this equation when we are given x only.

For instance,say x=a, is given to us, (which infact itself is a line) now this line intersects the line belonging to the family of line x=y+k, and the points of intersection gives us y and k,

But this line will intersect infinitely many lines belonging to that family, hence its not possible to fetch a unique solution.