Solve the linear system by using the substitution method. Describe the solu \[ \begin{array}{l}3 x+y=8 \\ 6 x+2 y=10\end{array} \] The system has \( \begin{array}{l}\text { no solution } \\ \text { one solution } \\ \text { infinite solutions }\end{array} \)

To solve the linear system using the substitution method, let's start with the first equation \(3x + y = 8\). We can express \(y\) in terms of \(x\): \[ y = 8 - 3x. \] Now, substitute this expression for \(y\) into the second equation \(6x + 2y = 10\): \[ 6x + 2(8 - 3x) = 10. \] Expanding this gives: \[ 6x + 16 - 6x = 10. \] This simplifies to: \[ 16 = 10. \] Since this is a contradiction (16 does not equal 10), the system has no solutions. The system of equations does not intersect at any point in a two-dimensional graph, meaning the two lines represented by these equations are parallel. Always remember that if you get a false statement when attempting to solve, it indicates there are no solutions!