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.

_______ named a point that is a solution that lies on the graph of the equation. _______ named a point that is not a solution and lies above the graph of the equation. _______ named a point that is not a solution and lies below the graph of the equation.

1 answer

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.

  1. Bella's point: \((-2, 1)\) \[ 2(-2) - 5(1) = -4 - 5 = -9 \quad \text{(not a solution)} \]

  2. Marco's point: \((11, 2)\) \[ 2(11) - 5(2) = 22 - 10 = 12 \quad \text{(not a solution)} \]

  3. 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.