To determine if the point \((5, 6)\) is a solution to the given system of equations, we need to substitute \(x = 5\) and \(y = 6\) into each equation and check if both equations hold true.
The equations given are:
- \(20x - 16y = 4\)
- \(6x + 19y = -5\)
Check the first equation:
Substitute \(x = 5\) and \(y = 6\):
\[ 20(5) - 16(6) = 4 \]
Calculating it step by step:
\[ 100 - 96 = 4 \] \[ 4 = 4 \quad \text{(True)} \]
Check the second equation:
Now substitute into the second equation:
\[ 6(5) + 19(6) = -5 \]
Calculating it step by step:
\[ 30 + 114 = -5 \] \[ 144 \neq -5 \quad \text{(False)} \]
Conclusion:
Since \((5, 6)\) satisfies the first equation but not the second, \((5, 6)\) is not a solution to the system of equations.