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?

For infinitely many solutions, the two equations must describe the same line. Rewrite the first equation: 3y + 12 = 6x gives y + 4 = 2x, so 2y = 4x − 8. Therefore b = −8, which is choice A.

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