A system of equations has definitely many solutions. If 2y-4x=6 is one of the equations, which could be the other equation?

The given equation is ⇒⇒⇒ 2y - 4x = 6

∴ 2y = 4x + 6 ⇒ divide all the equation over 2

∴ y = 2x + 3 and it can be written as ⇒⇒⇒ y - 2x = 3

The last equation represents a straight line with a slope = 2 and y-intercept = 3

To construct a system of equations with definitely many solutions and the equation (2y-4x=6) is one of the equations, the other equation must have the same slope and the same y-intercept.

so, the general solution of the other equation is ⇒ a (y - 2x) = 3a

Where a is constant and belongs to R (All real numbers)

The system of equations which has definitely many solutions is consisting of Coincident lines.