SAT Systems of two linear equations in two variables Practice Question 15 (Hard)

Question bank / Systems of two linear equations in two variables

Math · AlgebraHard

$ax + 3y = 12$
$4x + 6y = b$
In the system of equations above, $a$ and $b$ are constants. If the system has infinitely many solutions, what is the value of $a + b$ ?

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Answer: 26

For infinitely many solutions, the second equation must be a multiple of the first. The $y$ -coefficients show the multiplier is $\frac{6}{3} = 2$ . So $4 = 2a$ , giving $a = 2$ , and $b = 2(12) = 24$ . Then $a + b = 26$ .

Using the multiplier in the wrong direction gives $a = 8$ and $b = 6$ , so $a + b = 14$ .

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