Check whether the ordered pair \( (5,6) \) is a solution of the system. \( -2 x+4 y=-14 \) \( 3 x+y=21 \) a no

To determine whether the ordered pair \( (5, 6) \) is a solution to the system of equations, we need to substitute \( x = 5 \) and \( y = 6 \) into both equations and check if they hold true. 1. **First equation:** \[ -2x + 4y = -14 \] Substituting \( x = 5 \) and \( y = 6 \): \[ -2(5) + 4(6) = -14 \] \[ -10 + 24 = -14 \] \[ 14 \neq -14 \] The first equation is not satisfied. 2. **Second equation:** \[ 3x + y = 21 \] Substituting \( x = 5 \) and \( y = 6 \): \[ 3(5) + 6 = 21 \] \[ 15 + 6 = 21 \] \[ 21 = 21 \] The second equation is satisfied. Since the ordered pair \( (5, 6) \) does not satisfy the first equation, it is not a solution to the system of equations. Thus, the answer is **no**.