own below have a solution? ExI \[ \begin{array}{l}y=5 x+12 \\ 10 x-2 y=1\end{array} \]

To determine if the system of equations has a solution, we can use substitution or elimination methods. Starting with the first equation \( y = 5x + 12 \), we can substitute it into the second equation \( 10x - 2y = 1 \). This gives us: \[ 10x - 2(5x + 12) = 1 \] Simplifying this, we get: \[ 10x - 10x - 24 = 1 \] \[ -24 = 1 \] This is a contradiction, which means that the system of equations has no solution. The two lines represented by these equations are parallel and will never intersect! To illustrate further, envision two parallel train tracks: they run alongside each other infinitely but never meet. This means there's no point at which both equations are satisfied simultaneously, confirming our earlier finding of no solution!