The graphs of the functions $y=k x+b$ and $y=b x+k$ intersect. Find the abscissa of the point of intersection.

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First method. The desired abscissa is the solution to the equation $k x + b = b x + k$. This equation can be simplified to: $(k - b) x = k - b$. Since the given graphs intersect (do not coincide), $k \neq b$, therefore $x = 1$.

Second method. Notice that $x = 1$ is a solution to the problem: when $x = 1$, both given linear functions take the same value $y = k + b$. Since their graphs intersect, meaning these lines have exactly one common point, there are no other solutions.

## Answer

$x = 1$.

## Problem