a teacher wrote the equation 3y + 12 = 6x on the board. for what value of b would the additional equation 2y…

Answer:

A. $b = - 8$

Explanation:

Step1: Rewrite the first equation in slope - intercept form.

Starting with $3y+12 = 6x$, we solve for $y$. First, subtract 12 from both sides: $3y=6x - 12$. Then divide by 3: $y = 2x-4$.

Step2: Rewrite the second equation in slope - intercept form.

Starting with $2y=4x + b$, divide by 2: $y = 2x+\frac{b}{2}$.

Step3: Determine the condition for infinitely many solutions.

A system of linear equations $y = m_1x + c_1$ and $y=m_2x + c_2$ has infinitely many solutions when $m_1=m_2$ and $c_1 = c_2$. Here, $m_1=m_2 = 2$. For $c_1 = c_2$, we set $-4=\frac{b}{2}$.

Step4: Solve for $b$.

Multiply both sides of the equation $-4=\frac{b}{2}$ by 2: $b=-8$.