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

Explanation:

Step1: Simplify first equation

Start with $3y + 12 = 6x$. Subtract 12 from both sides:
$3y = 6x - 12$
Divide by 3:
$y = 2x - 4$

Step2: Simplify second equation

Start with $2y = 4x + b$. Divide by 2:
$y = 2x + \frac{b}{2}$

Step3: Match constants for infinite solutions

For infinite solutions, the constant terms must be equal:
$\frac{b}{2} = -4$
Solve for $b$:
$b = -4 \times 2 = -8$

Answer:

A. $b = -8$