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

Explanation:

Step1: Rewrite given equation in slope - intercept form

Given $4x - y=5$, we can rewrite it as $y = 4x - 5$. The slope of this line is $m_1 = 4$ and the y - intercept is $b_1=-5$.

Step2: Analyze each option

Option 1: $y=-4x + 5$

The slope $m=-4\neq4$, so it will intersect the line $y = 4x - 5$ at a single point.

Option 2: $y = 4x - 5$

This is the same line as the rewritten given line, so the system has infinitely many solutions.

Option 3: $2y=8x - 10$

Rewrite it as $y = 4x-5$, same as the given line, infinite solutions.

Option 4: $-2y=-8x - 10$

Rewrite it as $y = 4x + 5$, has the same slope as the given line ($m = 4$), so it is parallel (or the same line in some cases, but here it has a different y - intercept), and the system has either 0 or infinitely many solutions.

Answer:

A. $y=-4x + 5$