A system of equations has infinitely many solutions. If 2y - 4x = 6 is one of the equations, which could be the other equation? y = 2x + 6 y = 4x + 6 - y = - 2x - 3 - y = - 4x + 6

Option C

If 2y - 4x = 6 is one of the equations, then the other equation is - y = - 2x - 3

Solution:

Given that,

A system of equations has infinitely many solutions

One of the equation is given as 2y - 4x = 6

We have to find the other equation

A system of equations has infinitely many solutions when the two lines representing the equations coincide. i. e. the two equations are the same or a multiple of each other.

Given one of the equation is 2y - 4x = 6

Take 2 as common term

2 (y - 2x) = 6

y - 2x = 3

y = 2x + 3

Multiply the above equation by - 1

-y = - 2x - 3

This is same as option 3

Thus the other equation is - y = - 2x - 3

Answer: the third option