Math: Algebra

SAT Question of the Day for November 1, 2026

The system of equations

7x + 3y = k

and

21x + 9y = 54

has infinitely many solutions, where

k

is a constant. What is the value of

k

A. $18$ Correct answer
B. $27$
C. $9$
D. $54$

Explanation

For infinitely many solutions, the two equations must be scalar multiples of each other. The second equation

21x + 9y = 54

equals

3(7x + 3y) = 54

, so

7x + 3y = 18

. Therefore

k

must equal

18

. Choosing

54

results from setting

k

equal to the constant on the right side of the second equation without dividing by the scale factor

3

. Choosing

27

comes from an arithmetic error such as dividing

54

2

instead of

3

. Choosing

9

results from dividing

54

6

or confusing the coefficient relationship.

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