a system of equations has 1 solution. if 4x - y = 5 is one of the equations, which could be the other…

Explanation:

Step1: Rearrange given equation

Given $4x - y=5$, we can rewrite it as $y = 4x - 5$. A system of linear - equations $y=m_1x + b_1$ and $y=m_2x + b_2$ has one solution when $m_1\neq m_2$.

Step2: Analyze each option

• Option 1: For $y=-4x + 5$, $m=-4$. Since $-4\neq4$, this could be the other equation.
• Option 2: For $y = 4x-5$, $m = 4$. The two lines are parallel (same slope), so no unique solution.
• Option 3: Rewrite $2y=8x - 10$ as $y = 4x-5$. Same slope as the given line, no unique solution.
• Option 4: Rewrite $-2y=-8x - 10$ as $y = 4x + 5$. Same slope as the given line in non - standard form, no unique solution.

Answer:

A. $y=-4x + 5$