Final answer:
The ordered pair (7, -5) is not a solution to the system of equations 7x+4y=29 and 2x-2y=19 because it only satisfies the first equation but not the second one.
Step-by-step explanation:
The question you've asked is about determining whether an ordered pair is a solution to a system of equations. The system provided consists of two equations: 7x+4y=29 and 2x-2y=19.
To verify if the ordered pair (7, -5) is a solution, we need to substitute x with 7 and y with -5 into both equations to see if the equations hold true.
- For the first equation, 7x+4y=29, substituting the ordered pair gives us 7(7) + 4(-5), which simplifies to 49 - 20, resulting in 29. This matches the value on the right side of the equation.
- For the second equation, 2x-2y=19, substituting the ordered pair gives us 2(7) - 2(-5), which simplifies to 14 + 10, also resulting in 24, not matching the value on the right side of the equation.
Since the second equation does not hold true with this ordered pair, (7, -5) is not a solution to the system of equations.