What are the solutions (x, y) of the system of equations shown?

Rationale

The solutions (x, y) of the system of equations are (-3, -5) and (1, 3).

These coordinates satisfy the equations in the system, making them the valid solutions. Checking each pair against the equations confirms their accuracy.

A ((- √(2), 0) and (√(2), 0)) YOUR ANSWER

This option represents two points along the x-axis, but substituting these values into the original equations does not satisfy the conditions set by the system. Thus, they cannot be valid solutions.

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

Similar to option A, this pair lies on the x-axis. However, neither of these points satisfies the given equations when substituted, ruling them out as solutions.

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

Though these points do provide specific coordinates, testing them in the original equations shows that they do not fulfill the requirements of the system. Therefore, they cannot be considered solutions.

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

While these points contain valid numeric coordinates, they fail to meet the criteria set by the system of equations upon substitution. Consequently, these pairs are not solutions.

Conclusion

The correct solutions for the system of equations are (-3, -5) and (1, 3), as they satisfy all criteria when checked against the original equations. Each of the other options fails to meet the system's requirements, confirming that only option E provides valid solutions.

What are the solutions (x, y) of the system of equations shown?

The solutions (x, y) of the system of equations are (-3, -5) and (1, 3).

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