6
AssignmentMultiple Choice

Solving Linear Systems by Substitution

Question 6 • EAP-Algebra Functions and Data Analysis A CR

Think about the graphs of the equations in the following system.x2+ y2 = 2y = 2x2 – 3Which of the following describes the system?

Answer
A
circle with its center at (0, 0) and a radius of ; parabola opening up with its vertex at (0, –3)
B
circle with its center at (0, 0) and a radius of ; parabola opening up with its vertex at (0, 3)
C
circle with its center at (0, 0) and a radius of 2; parabola opening up with its vertex at (0, –3)
D
circle with its center at (0, 0) and a radius of 2; parabola opening up with its vertex at (0, 3)

Explanation

The equation x² + y² = 2 is a circle centered at (0, 0), since it has the form x² + y² = r². Here r² = 2, so the radius is √2. The equation y = 2x² − 3 is an upward-opening parabola because the coefficient of x² is positive, and its vertex is (0, −3). These descriptions match choice A.

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