To determine which students named solutions or points relative to the equation \(2x - 5y = 9\), we need to substitute their points into the equation and see if they satisfy it.
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Bella's point: \((-2, 1)\) \[ 2(-2) - 5(1) = -4 - 5 = -9 \quad \text{(not a solution)} \]
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Marco's point: \((11, 2)\) \[ 2(11) - 5(2) = 22 - 10 = 12 \quad \text{(not a solution)} \]
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Liam's point: \((2, -1)\) \[ 2(2) - 5(-1) = 4 + 5 = 9 \quad \text{(is a solution)} \]
Now, we analyze each student's claim regarding their points:
- Liam named a point that is a solution that lies on the graph of the equation.
- Bella named a point that is not a solution and lies below the graph of the equation (since -9 is less than 9).
- Marco named a point that is not a solution and lies above the graph of the equation (since 12 is greater than 9).
Thus, we can fill in the blanks:
- Liam named a point that is a solution that lies on the graph of the equation.
- Bella named a point that is not a solution and lies below the graph of the equation.
- Marco named a point that is not a solution and lies above the graph of the equation.