Is (7, 3) the solution to the system of these linear equations: 3x+2y=5 and −x+6y=11? Why?

1 answer

To determine if the point (7, 3) is a solution to the system of equations \(3x + 2y = 5\) and \(-x + 6y = 11\), we need to substitute \(x = 7\) and \(y = 3\) into both equations and check if they hold true.

  1. Substituting into the first equation:

    \[ 3x + 2y = 5 \]

    Substituting \(x = 7\) and \(y = 3\):

    \[ 3(7) + 2(3) = 21 + 6 = 27 \]

    Since \(27 \neq 5\), the first equation is not satisfied.

  2. Substituting into the second equation:

    \[ -x + 6y = 11 \]

    Substituting \(x = 7\) and \(y = 3\):

    \[ -7 + 6(3) = -7 + 18 = 11 \]

    In this case, the second equation is satisfied.

Since the point (7, 3) does not satisfy the first equation, it is not a solution to the system of equations. Thus, the answer is No, (7, 3) is not a solution to the system.