Question #adb0c96c - SAT Suite Question Bank

ID: adb0c96c

Modded SAT Question Bank by Abdullah Mallik

$24 x + y = 48$

$6 x + y = 72$

The solution to the given system of equations is $(x, y)$ . What is the value of $y$ ?

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Correct Answer: 80

Rationale

The correct answer is $80$ . Subtracting the second equation in the given system from the first equation yields $(24 x + y) - (6 x + y) = 48 - 72$ , which is equivalent to $24 x - 6 x + y - y = - 24$ , or $18 x = - 24$ . Dividing each side of this equation by $3$ yields $6 x = - 8$ . Substituting $negative 8$ for $6 x$ in the second equation yields $- 8 + y = 72$ . Adding $8$ to both sides of this equation yields $y equals 80$ .

Alternate approach: Multiplying each side of the second equation in the given system by $4$ yields $24 x + 4 y = 288$ . Subtracting the first equation in the given system from this equation yields $(24 x + 4 y) - (24 x + y) = 288 - 48$ , which is equivalent to $24 x - 24 x + 4 y - y = 240$ , or $3 y equals 240$ . Dividing each side of this equation by $3$ yields $y equals 80$ .

Question Difficulty: Hard