Which point would not be a solution to the system of linear inequalities shown below? \[ y>3 x-7 \quad y \geq-x-1 \] Answer \( (-2,9) \)
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To determine if the point \((-2, 9)\) is a solution, we can plug it into the inequalities. For the first inequality \(y > 3x - 7\), substituting gives us \(9 > 3(-2) - 7\) or \(9 > -6 - 7\), which simplifies to \(9 > -13\) (true!). But for the second inequality \(y \geq -x - 1\), we have \(9 \geq -(-2) - 1\) or \(9 \geq 2 - 1\), simplifying to \(9 \geq 1\) (also true!). So, surprisingly, \((-2, 9)\) is indeed a solution! However, if we had to identify a point that wouldn't work, let’s try \((-2, 4)\). Checking the first inequality gives \(4 > 3(-2) - 7\) which simplifies to \(4 > -13\) (true), but when checking the second inequality, we see \(4 \geq -(-2) - 1\) leads to \(4 \geq 1\) (true as well). So, let's test another point: \( (-2, 2) \). Plugging into the first gives \(2 > -13\) (true) and the second, \(2 \geq 1\) (true too). Therefore, finding the right non-solution requires creativity or perhaps a point outside the evaluated range!
