2x + y = 11 x = 3y + 2 Which ordered pair (x, y) is the... | SAT Systems of two linear equations in two variables Question, Answer Explained

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$2x + y = 11$
$x = 3y + 2$
Which ordered pair $(x, y)$ is the solution to the system of equations?

$(1, 5)$

$(2, 0)$

$(4, 3)$

$(5, 1)$

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Answer: D

Substitute $3y + 2$ for $x$ in the first equation: $2(3y + 2) + y = 11$ , so $7y + 4 = 11$ and $y = 1$ . Then $x = 3(1) + 2 = 5$ . Check: $2(5) + 1 = 11$ .

Choice C satisfies the first equation, but $3(3) + 2 = 11$ , not $4$ , so it fails the second equation.

Why the other choices are wrong

A. This switches x and y. The point (1, 5) doesn't satisfy x = 3y + 2.
B. (2, 0) satisfies x = 3y + 2, but 2(2) + 0 = 4, not 11.
C. (4, 3) satisfies 2x + y = 11, but 3(3) + 2 = 11, not 4.

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