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Ms. Mac asked her students to determine a solution for 2x - 5y = 9. Bella believes (-2, 1) is a solution to the equation. Marco believes (11, 2) is a solution to the equation. Liam believes (2, -1) is a solution to the equation.

3 answers

To determine if each of the provided points is a solution to the equation \(2x - 5y = 9\), we will substitute the \(x\) and \(y\) values from each point into the equation and see if the equation holds true.

  1. For Bella's point (-2, 1): \[ x = -2, \quad y = 1 \] Substitute into the equation: \[ 2(-2) - 5(1) = -4 - 5 = -9 \] Since \(-9 \neq 9\), Bella's point is not a solution.

  2. For Marco's point (11, 2): \[ x = 11, \quad y = 2 \] Substitute into the equation: \[ 2(11) - 5(2) = 22 - 10 = 12 \] Since \(12 \neq 9\), Marco's point is not a solution.

  3. For Liam's point (2, -1): \[ x = 2, \quad y = -1 \] Substitute into the equation: \[ 2(2) - 5(-1) = 4 + 5 = 9 \] Since \(9 = 9\), Liam's point is a solution.

In summary:

  • Bella's point (-2, 1) is not a solution.
  • Marco's point (11, 2) is not a solution.
  • Liam's point (2, -1) is a solution.
is Bella and Marcos solution below or above the graph

To determine whether Bella's and Marco's points lie above or below the graph of the equation \(2x - 5y = 9\), we can evaluate the equation at their \(x\) values and compare the corresponding \(y\) values.

  1. For Bella's point (-2, 1):

    • Calculate the \(y\) value on the line when \(x = -2\): \[ 2(-2) - 5y = 9 \implies -4 - 5y = 9 \implies -5y = 13 \implies y = -\frac{13}{5} \approx -2.6 \]
    • Bella's \(y\) value is 1, while the calculated \(y\) value on the line is approximately -2.6.
    • Since \(1 > -2.6\), Bella's point (-2, 1) lies above the graph of the equation.

  2. For Marco's point (11, 2):

    • Calculate the \(y\) value on the line when \(x = 11\): \[ 2(11) - 5y = 9 \implies 22 - 5y = 9 \implies -5y = -13 \implies y = \frac{13}{5} \approx 2.6 \]
    • Marco's \(y\) value is 2, while the calculated \(y\) value on the line is approximately 2.6.
    • Since \(2 < 2.6\), Marco's point (11, 2) lies below the graph of the equation.

In summary:

  • Bella's point (-2, 1) is above the graph.
  • Marco's point (11, 2) is below the graph.