Which best describes a system of equations that has infinitely many solutions

see explanation

Step-by-step explanation:

Either both equations are equal or are multiples of each other

As an example consider the 2 equations

4x - y = 2 → (1)

- 12x + 3y = - 6 → (2)

Multiply (1) by - 3

- 12x + 3y = - 6 → (3)

Subtract (3) from (2) term by term

(- 12x - (- 12)x) + (3y - 3y) = (- 6 - (- 6)), that is

(- 12x + 12x) + 0 = - 6 + 6

0 = 0

This indicates the solution has infinite solutions

let x = k, k is a real number then from (1) y = 4x - 2 ⇒ y = 4k - 2

Thus (k, 4k - 2) will generate solutions to the system of equations