Question 26

The solutions (x, y) of the system of equations are (-1, -1) and (3, 7).

The solutions to the system of equations provided in the question are indeed (-1, -1) and (3, 7), which satisfy both equations within the system.

A) (-√2, 0) and (√2, 0)

This option represents two points on the x-axis. However, these points do not satisfy the equations of the system, as the y-values are not taken into account, leading to an incorrect solution set.

B) (-1/2, 0) and (2, 0)

Similar to option A, this choice consists of points solely on the x-axis. Neither (-1/2, 0) nor (2, 0) meets the criteria set by the equations in the system, making this option incorrect.

C) (-1, -1) and (3, 7)

This option is correct, as both points satisfy the equations in the system. When plugging (-1, -1) and (3, 7) into the equations, they yield valid results, confirming these as the correct solutions.

D) (-1, 1) and (3, -7)

While this option provides two points, neither of these points satisfies the equations of the system. Thus, this option is incorrect, as it does not yield valid solutions.

E) (-3, -5) and (1, 3)

This option presents two arbitrary points that do not satisfy the equations in the system. Therefore, it is also incorrect, as these points do not meet the requirements to be the solutions of the system.

Conclusion

The option C, which includes the pairs (-1, -1) and (3, 7), is definitively correct because both solutions satisfy the given system of equations. All other options fail to provide points that adhere to the equations, confirming their incorrectness in this context.