Question

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

Explanation:

Step1: Rewrite 2nd equation in slope-intercept form

Start with $4x + 2y = 8$. Isolate $y$:
Subtract $4x$: $2y = -4x + 8$
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 $b_1=b_2$. Here, $m_1=m_2=-2$, so set $b=4$.

Answer:

4 (Option C)