To determine if \((8, 2)\) is a solution to the system of equations given by:
- \(x + y = 10\)
- \(6x + 4y = 19\)
we can substitute \(x = 8\) and \(y = 2\) into both equations.
For the first equation: \[ 8 + 2 = 10 \] This is true, as \(10 = 10\).
For the second equation: \[ 6(8) + 4(2) = 19 \] Calculate the left side: \[ 48 + 8 = 56 \] So, \(56\) does not equal \(19\).
Since \((8, 2)\) satisfies the first equation but not the second, we can conclude that \((8, 2)\) is not a solution to the system of equations.