SAT Math Question for the week of 07/04/2021

bx + 8y = c

5x + 8y = 2c

In the system of equations above, for which of the following values of b does the system have no solution, where b and c are constants?

A) 1

B) 3

C) 4

D) 5

Maps to Category 9 of the book.

There is a flashcard for this concept accessible from the Resources page.

Answer posted on 07/11/2021: Correct answer choice is D.

Detailed Solution

Solution without calculation: This question can also be solved without any calculation. See logic below.

In both the equations, the coefficient of b is same. For the system to have no solution, the coefficient of a must also be same in both the equations. Hence, the coefficient of a must be 5 in both the equations.