y = x^2 + 1 y = 5 Which ordered pair (x, y) is a solution to... | SAT Nonlinear equations in one variable and systems of equations in two variables Question, Answer Explained

Math · Advanced MathEasy

$y = x^2 + 1$
$y = 5$
Which ordered pair $(x, y)$ is a solution to the system of equations?

$(2, 5)$

$(4, 5)$

$(5, 2)$

$(5, 26)$

Show answer and explanation

Answer: A

Substitute $y = 5$ into the first equation: $5 = x^2 + 1$ , so $x^2 = 4$ and $x = 2$ or $x = -2$ . So $(2, 5)$ is a solution.

Choice B uses $x^2 = 4$ but forgets to take the square root.

Why the other choices are wrong

B. 4 is the value of x², not x. Taking the square root gives x = 2 or x = -2.
C. This switches the coordinates. In the solution, y = 5 and x = 2.
D. This substitutes 5 for x in the first equation. The second equation says y, not x, equals 5.

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