Question

Which of the following systems of equations has no solution?

a. 9x + 5y = 1; 15y = 18x − 4
b. -7x − 7 = 3y; -14y − 8 = -6x
c. 4x − 3y = 9; 6y = 8x − 18
d. 7y = 5x − 10; 10x − 14y = 8

Answer 1

The system of equations that has no solution are the equations that has the same slope which means they are parallel and do not intersect with each other at any point. From the choices, the correct answer is option D.

7y = 5x − 10
y = (5/7) - 10/7
slope = 5/7

10x − 14y = 8
-14y = -10x + 8
y = (5/7) - 4/7
slope = 5/7

Answer 2

For option d:
5x - 7y = 10 . . . . . (1)
10x - 14y = 8 . . . . (2)

(1) x 2 => 10x - 14y = 20 . . . . . (3)

(2) - (3) => 0 = -14 [not possible]

Therefore, the set of equations in option d, has no solutions.