To determine which ordered pair lies on the graph of the equation \(2X - 5Y = 12\), we will substitute the \(X\) and \(Y\) values of each pair into the equation and see if the equation is satisfied (i.e., if the left side equals the right side).
A: \((3, -\frac{6}{5})\)
Substituting \(X = 3\) and \(Y = -\frac{6}{5}\): \[ 2(3) - 5\left(-\frac{6}{5}\right) = 6 + 6 = 12 \] This pair satisfies the equation.
B: \((1, 2)\)
Substituting \(X = 1\) and \(Y = 2\): \[ 2(1) - 5(2) = 2 - 10 = -8 \quad \text{(not equal to 12)} \]
C: \((0, \frac{12}{5})\)
Substituting \(X = 0\) and \(Y = \frac{12}{5}\): \[ 2(0) - 5\left(\frac{12}{5}\right) = 0 - 12 = -12 \quad \text{(not equal to 12)} \]
D: \((-1, -2)\)
Substituting \(X = -1\) and \(Y = -2\): \[ 2(-1) - 5(-2) = -2 + 10 = 8 \quad \text{(not equal to 12)} \]
The ordered pair that lies on the graph of the equation \(2X - 5Y = 12\) is:
A: \((3, -\frac{6}{5})\)