Find the solution of the system of equations. \[ \begin{array}{r}8 x+y=17 \\ 4 x+3 y=31\end{array} \]

To solve the system of equations, we can use the method of substitution or elimination. Let's use substitution for this example. From the first equation, we can express \( y \) in terms of \( x \): \[ y = 17 - 8x. \] Now, we can substitute this expression for \( y \) into the second equation: \[ 4x + 3(17 - 8x) = 31. \] Distributing the \( 3 \): \[ 4x + 51 - 24x = 31. \] Now, combine the terms: \[ -20x + 51 = 31. \] Next, isolate \( x \): \[ -20x = 31 - 51, \] \[ -20x = -20, \] \[ x = 1. \] Now that we have \( x \), we can substitute it back into the equation for \( y \): \[ y = 17 - 8(1) = 17 - 8 = 9. \] Thus, the solution to the system of equations is \[ (x, y) = (1, 9). \]