To determine if the point \((1, 4)\) is a solution to the system of equations, we need to check whether it satisfies both equations:
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First equation: \(y = x + 9\)
- Substitute \(x = 1\): \[ y = 1 + 9 = 10 \]
- We found that when \(x = 1\), \(y\) should be \(10\). However, we have \(y = 4\) in the point \((1, 4)\), so this equation is not satisfied.
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Second equation: \(y = 10x + 7\)
- Again, substitute \(x = 1\): \[ y = 10(1) + 7 = 10 + 7 = 17 \]
- Here, when \(x = 1\), \(y\) should be \(17\). This again does not match, as we have \(y = 4\) in the point \((1, 4)\).
Since \((1, 4)\) does not satisfy either of the equations in the system, we conclude that:
\((1, 4)\) is not a solution to the system of equations.