which equation, when paired with y = 2x + 5, creates an inconsistent system?\n2x + y = 5\ny = 2x + 5\n2x…

Explanation:

Step1: Recall the condition for an inconsistent system

An inconsistent system of linear - equations has no solution, which means the two lines are parallel (same slope but different y - intercepts). The given equation is $y = 2x+5$, and its slope $m = 2$ and y - intercept $b = 5$.

Step2: Rewrite each option in slope - intercept form ($y=mx + b$)

• Option 1: $2x + y=5$ can be rewritten as $y=-2x + 5$. The slope is $m=-2$.
• Option 2: $y = 2x+5$ has a slope $m = 2$ and y - intercept $b = 5$, same as the given line (it's the same line, not an inconsistent system).
• Option 3: $2x-4y = 10$ can be rewritten as $-4y=-2x + 10$, then $y=\frac{1}{2}x-\frac{5}{2}$. The slope is $m=\frac{1}{2}$.
• Option 4: $2y-4x=-10$ can be rewritten as $2y=4x - 10$, then $y = 2x-5$. The slope is $m = 2$ and y - intercept $b=-5$. Since it has the same slope as $y = 2x + 5$ but a different y - intercept, it forms an inconsistent system with $y = 2x+5$.

Answer:

D. $2y-4x=-10$