To determine which of the points mentioned are solutions to the equation \(2x - 5y = 9\), we can substitute the coordinates into the equation.
Testing Bella's solution (-2, 1):
Substituting \(x = -2\) and \(y = 1\): \[ 2(-2) - 5(1) = -4 - 5 = -9 \quad (\text{not } 9) \] So, (-2, 1) is not a solution.
Testing Marco's solution (11, 2):
Substituting \(x = 11\) and \(y = 2\): \[ 2(11) - 5(2) = 22 - 10 = 12 \quad (\text{not } 9) \] So, (11, 2) is not a solution.
Testing Liam's solution (2, -1):
Substituting \(x = 2\) and \(y = -1\): \[ 2(2) - 5(-1) = 4 + 5 = 9 \quad (\text{is } 9) \] So, (2, -1) is a solution.
Conclusion:
- Bella's point, \((-2, 1)\), is not a solution and lies above the graph because it yields \(-9\) which is less than \(9\).
- Marco's point, \((11, 2)\), is not a solution and lies above the graph because it yields \(12\) which is greater than \(9\).
- Liam's point, \((2, -1)\), is a solution that lies on the graph.
Inserting Responses:
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Point that is a solution that lies on the graph of the equation: (2, -1)
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Point that is not a solution and lies above the graph of the equation: (11, 2)
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Point that is not a solution and lies below the graph of the equation: (-2, 1)
You can now select and insert those responses where they belong!
1 answer