Which value, when placed in the box, would result in a system of equations with infinitely many solutions?

y = 2x - 5

2y - 4x =

a. - 10

b. - 5

c. 5

d. 10

For a system of equations to have infinitely many solutions, the equations have to be lineary dependent, (i. e. one of the equations is a multiple of the other equation). For the given equation to have infinitely many solutions, the second equation have to be a multiple of the first equation. The first equation can be rewritten as y - 2x = - 5 The second equation is the first equation multiplied by 2, i. e. 2 (y - 2x = - 5) = 2y - 4x = - 10 Therefore, the correct answer is - 10 (option a).