To determine if the point (2, 6) is a solution to the given system of equations, we need to substitute \( x = 2 \) and \( y = 6 \) into each equation and check if both equations hold true.
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First Equation: \( y = \frac{3}{2}x + 3 \)
Substitute \( x = 2 \):
\[ y = \frac{3}{2}(2) + 3 \]
\[ y = 3 + 3 = 6 \]
So, the point (2, 6) satisfies the first equation.
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Second Equation: \( y = -9x + 1 \)
Substitute \( x = 2 \):
\[ y = -9(2) + 1 \]
\[ y = -18 + 1 = -17 \]
Here, \( y \) does not equal 6; it equals -17.
Since (2, 6) satisfies the first equation but not the second, it is not a solution to the system of equations.