Question when-t
When the equations above are graphed in the xy-plane, what are the coordinates (x, y) of the points of intersection of the two graphs?
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When the equations above are graphed in the xy -plane, what are the coordinates ( x
Hard-difficulty · SAT Math · Systems Involving Nonlinear Equations — Substitution/elimination with nonlinear components. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice A is correct. The two equations form a system of equations, and the solutions to the system correspond to the points of intersection of the graphs. The solutions to the system can be found by substitution. Since the second equation gives y = 3, substituting 3 for y in the first equation gives 3 = x2 – 1. Adding 1 to both sides of the equation gives 4 = x2. Solving by taking the square root of both sides of the equation gives x = ±2. Since y = 3 for all values of x for the second equation, the solutions are (2, 3) and (–2, 3). Therefore, the points of intersection of the two graphs are (2, 3) and (–2, 3).
Choices B, C, and D are incorrect and may be the result of calculation errors.
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