Question

what value of b will make the system of equations have an infinite number of solutions?\
y = -2x + b\
4x + 2y = 8\
\bigcirc 2\
\bigcirc 8\
\bigcirc 4\
\bigcirc -4

Explanation:

Step1: Rewrite second equation to slope-intercept form

Start with $4x + 2y = 8$. Subtract $4x$ from both sides:
$2y = -4x + 8$
Divide by 2:
$y = -2x + 4$

Step2: Match coefficients for infinite solutions

For two linear equations $y = m_1x + b_1$ and $y = m_2x + b_2$ to have infinite solutions, $m_1=m_2$ and $b_1=b_2$. The first equation is $y=-2x+b$, so set $b=4$.

Answer:

○ 4