Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.

-x+6y=9
-4x+24y=48

Answer 1

no solution

Explanation:

- x + 6y = 9 → (1)

- 4x + 24y = 48 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x and y

4x - 24y = - 36 → (3)

add (2) and (3) term by term

0 + 0 = 12

0 = 12 ← false statement

this false statement indicates the system has no solution