ax + by = 13 bx + ay = 17 In the system of equations, a and b... | SAT Systems of two linear equations in two variables Question, Answer Explained

Question bank / Systems of two linear equations in two variables

Math · AlgebraHard

$ax + by = 13$
$bx + ay = 17$
In the system of equations, $a$ and $b$ are constants. If $(2, 3)$ is a solution to the system, what is the value of $a + b$ ?

Student-produced response: enter your answer.

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Answer: 6

Substitute $x = 2$ and $y = 3$ : $2a + 3b = 13$ and $2b + 3a = 17$ . Adding these equations gives $5a + 5b = 30$ , so $a + b = 6$ . Solving fully gives $a = 5$ and $b = 1$ , which agrees.

Answering $5$ gives the value of $a$ alone, not $a + b$ .

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