*bx + *8*y = c*

* *5*x + *8*y = *2*c*

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.