A teacher wrote the equation 3y + 12 = 6x on the board. For what value of b would the additional equation 2y = 4x + b form a system of linear equations with infinitely many solutions? b = –8
b = –4
b = 2
b = 6

-8

Step-by-step explanation:

For a system to have infinitely many solutions the two equations must be the same line. We can simplify the first and second equations by dividing them by 3 and 2 respectively to get:

y + 4 = 2x

y = 2x + b/2 → y -b/2 = 2x

Since the constants must be equal, 4 = -b/2 which means b = -8.