Question

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

Answer 1

-10

Explanation:

Answer 2

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).