Question

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?
$b = -8$
$b = -4$
$b = 2$
$b = 6$

Explanation:

Step1: Simplify first equation

Rearrange $3y + 12 = 6x$ to slope-intercept form:
Subtract 12 from both sides: $3y = 6x - 12$
Divide by 3: $y = 2x - 4$
Multiply by 2 to match coefficient of $y$ in second equation: $2y = 4x - 8$

Step2: Compare to second equation

The second equation is $2y = 4x + b$. For infinitely many solutions, the two equations must be identical, so their constant terms must be equal.
Set $-8 = b$

Answer:

A. $b = -8$