What are the solutions (x, y) of the system of equations shown?
(-1, -1) and (3, 7) are the solutions to the system of equations.
The given system of equations can be solved by substitution or elimination methods, leading us to the pairs (-1, -1) and (3, 7) as the correct solutions that satisfy both equations simultaneously.
This choice represents points that do not satisfy the equations. Substituting these values into the original equations reveals that neither point meets the criteria established by the system, hence they are not solutions.
Similar to choice A, these points are not valid solutions for the system of equations. Evaluating them in the equations shows discrepancies that render them invalid as solutions, confirming they do not satisfy the conditions required.
This is the correct answer as both pairs satisfy the equations when substituted. They meet the conditions set forth by the system of equations, making them valid solutions.
This option also fails to satisfy the original equations. Substituting these values results in contradictions, showing that they do not hold true for the system, thus excluding them as potential solutions.
Lastly, these points do not fulfill the requirements of the given equations. Testing them in the system shows they do not satisfy the equations, confirming their status as incorrect solutions.
The evaluation of the system of equations confirms that (-1, -1) and (3, 7) are the only pairs that satisfy both equations, thereby making them the correct solutions. The other options failed upon substitution, illustrating that they do not fit the established criteria of the problem. This process emphasizes the importance of validating solutions through direct substitution into the equations.
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