Question

Determine if the system of equations has one solution, no solution or infinitely many solutions. Make sure to show all your work to receive full credit for each question.

-3x+12y=12

x-4y=-4

Show your work by including a written or verbal explanation of WHY your answer includes one solution, no solution or infinitely many solutions.

Answer 1

Answer:

Step-by-step explanation:

-3x + 12y = 12

=> 3x - 12y + 12 = 0   ----------------- (1)

x - 4y = -4

=> x - 4y + 4 = 0         ------------------(2)

These equations are of the following form:

a₁x + b₁y + c₁ = 0 , a₂x + b₂y + c₂ = 0

Here a₁ = 3, b₁ = -12, c₁ = 12

         a₂ = 1, b₂ = -4, c₂ = 4

∴ a₁/a₂ = 3/1 = 3

  b₁/b₂ = -12/-4 = 3

  c₁/c₂  = 12/4 = 3

Thus, a₁/a₂ = b₁/b₂ = c₁/c₂.

Hence the given system of equations has infinite number of solutions.