Final answer:
The ordered pair (10, 5) is not a solution to either equation in the given system. Substituting the values into the equations shows that the pair does not satisfy either equation, making it not a solution to the system. The correct answer is option: c) The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair 10 comma 5 end ordered pair, is not a solution to the system because it makes at least one of the equations false.
Step-by-step explanation:
To determine whether the ordered pair (10, 5) is a solution to the system of equations, we must substitute x with 10 and y with 5 into each equation and see if the equations hold true.
- First equation: 2x - 5y = 0
Substitute (10, 5): 2(10) - 5(5) = 20 - 25 = -5
The equation does not hold true; therefore, the ordered pair (10, 5) is not a solution to the first equation.
- Second equation: -5x + 2y = 11
Substitute (10, 5): -5(10) + 2(5) = -50 + 10 = -40
The equation does not hold true; thus, the ordered pair (10, 5) is not a solution to the second equation.
Since the ordered pair does not solve either equation, it cannot be a solution to the system. The statement that (10, 5) is not a solution to the system because it makes at least one of the equations false is, in fact, true.