Solve for \( x \) and \( y \) \( 3 x-2 y=8 \) \( 4 x-2 y=6 \)

To solve the system of equations 1. \( 3x - 2y = 8 \) 2. \( 4x - 2y = 6 \) we can start by eliminating \( y \). By subtracting the first equation from the second, we get: \[ (4x - 2y) - (3x - 2y) = 6 - 8 \] This simplifies to: \[ 4x - 3x = -2 \] which gives: \[ x = -2 \] Now, we can substitute \( x = -2 \) back into one of the original equations to find \( y \). We'll use the first equation: \[ 3(-2) - 2y = 8 \] This simplifies to: \[ -6 - 2y = 8 \] Adding 6 to both sides gives: \[ -2y = 14 \] Dividing by -2 results in: \[ y = -7 \] Thus, the solution is \( x = -2 \) and \( y = -7 \).