A system of two linear equations has infinitely many solutions. One equation is x - 2y=6. Select the equation that would make this system have infinitely many solutions.

A .x + 2y = 6

B .x-2y = 4

C . 2y-x= -6

D .- 2y + x=4

C . 2y-x= -6

Step-by-step explanation:

A system of linear equations can have no solution, a unique solution or infinitely many solution.

We say two linear equations has infinitely many solutions when the result is true.

To determine if a system has infinitely many solutions, the coefficient of their respective variables (x and y) would be equal. Also the constant of both equations would be equal.

Given that x - 2y = 6

The coefficient of x is 1, coefficient of y is -2 and constant is 6. The equation with the same attributes is:

C . 2y-x= -6

2y - x = -6

multiply through by -1

x - 2y = 6

It is same as the above

Adding both x - 2y = 6 and 2y-x= -6 gives 0 = 0