Asked by kasdfa
Which of the following graphs represents the solution(s) of the following system?
x2 + y = 7
x2 + y2 = 49
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the equations as x^2 + y = 7 and x^2 + y^2 = 49.
From the first, y = 7 − x^2. Substitute into the circle:
x^2 + (7 − x^2)^2 = 49
x^4 − 13x^2 = 0
x^2(x^2 − 13) = 0
So x = 0 or x = ±√13. The corresponding y values are
- x = 0 → y = 7
- x = ±√13 → y = 7 − 13 = −6
Thus the system has three solutions: (0, 7) and (±√13, −6). The correct graph is the circle x^2 + y^2 = 49 and the downward parabola y = 7 − x^2 intersecting at those three points.
From the first, y = 7 − x^2. Substitute into the circle:
x^2 + (7 − x^2)^2 = 49
x^4 − 13x^2 = 0
x^2(x^2 − 13) = 0
So x = 0 or x = ±√13. The corresponding y values are
- x = 0 → y = 7
- x = ±√13 → y = 7 − 13 = −6
Thus the system has three solutions: (0, 7) and (±√13, −6). The correct graph is the circle x^2 + y^2 = 49 and the downward parabola y = 7 − x^2 intersecting at those three points.
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