20. \( \left\{\begin{array}{l}-4 m+3 n-6=0 \\ n=\frac{-1}{3} m-8\end{array}\right. \)

To solve the system of equations, we can use substitution or elimination. Let's substitute the expression for \( n \) from the second equation into the first equation: 1. Substitute: \[ -4m + 3\left(\frac{-1}{3}m - 8\right) - 6 = 0 \] 2. Simplify: \[ -4m - m - 24 - 6 = 0 \] \[ -5m - 30 = 0 \] 3. Solve for \( m \): \[ -5m = 30 \] \[ m = -6 \] 4. Now substitute \( m = -6 \) back into the second equation to find \( n \): \[ n = \frac{-1}{3}(-6) - 8 \] \[ n = 2 - 8 \] \[ n = -6 \] Thus, the solution to the system of equations is \( m = -6 \) and \( n = -6 \). --- The values we found can be represented as the point \( (-6, -6) \), which means that both variables share the same value in this particular case, intersecting at a unique point on the coordinate plane. This unique solution indicates that the two lines represented by the equations are not parallel and intersect at precisely this point! If you're ever unsure about your steps, it’s helpful to graph the equations! Visualizing them can often clarify intersections and why certain solutions are valid. Don’t be afraid of making mistakes; they’re often the best teachers!