Solve the following system of equations: x - 2y = 8, x - 3y = 6.

Okay, let's solve the system of equations: \[ \begin{cases} x - 2y = 8 \\ x - 3y = 6 \end{cases} \] We can use the method of substitution or elimination. Let's use the elimination method. **Step 1: Elimination** Subtract the second equation from the first equation to eliminate (x): \[ (x - 2y) - (x - 3y) = 8 - 6 \] \[ x - 2y - x + 3y = 2 \] \[ y = 2 \] **Step 2: Substitution** Now that we have the value of (y), substitute it into one of the original equations to find (x). Let's use the first equation: \[ x - 2(2) = 8 \] \[ x - 4 = 8 \] \[ x = 8 + 4 \] \[ x = 12 \] **Solution** So the solution to the system of equations is (x = 12) and (y = 2). \[ \begin{cases} x = 12 \\ y = 2 \end{cases} \] **Final Answer:** The solution is (x = 12) and (y = 2).