7. \( \begin{aligned}-3 x+y & =-8 \\ 4 x+3 y & =28\end{aligned} \)

To solve the system of equations, we can use the substitution or elimination method. Here’s a fun approach using elimination! First, we can manipulate the first equation, \( -3x + y = -8 \), to express \( y \) in terms of \( x \): \[ y = 3x - 8. \] Now we can substitute this expression for \( y \) into the second equation, \( 4x + 3y = 28 \): \[ 4x + 3(3x - 8) = 28. \] Expanding and simplifying gives: \[ 4x + 9x - 24 = 28 \quad \Rightarrow \quad 13x - 24 = 28 \quad \Rightarrow \quad 13x = 52 \quad \Rightarrow \quad x = 4. \] Now, substituting \( x = 4 \) back into \( y = 3x - 8 \): \[ y = 3(4) - 8 = 12 - 8 = 4. \] The solution to the system is \( x = 4 \), \( y = 4 \) or the point (4, 4). Voila! 🎉