To form a system that has no solution, the two equations must represent parallel lines, which means they have the same slope but different y-intercepts.
The given equation is: \[ y = 5x - 10 \]
The slope of this line is 5. Now, let's analyze the options:
A. \( y = -5x + 10 \)
- Slope = -5 (Different slope, so this is not parallel)
B. \( y = 5(x + 2) = 5x + 10 \)
- Slope = 5 (Same slope, but different y-intercept, so this is parallel)
C. \( y = 5(x - 2) = 5x - 10 \)
- Slope = 5 (Same slope and same y-intercept, so this is the same line)
D. \( y = -5x - 10 \)
- Slope = -5 (Different slope, so this is not parallel)
The only equation that has the same slope (5) but a different y-intercept is option B. Therefore, when graphed with the given equation, \( y = 5(x + 2) \) will form a system that has no solution.
The correct answer is: B. \( y = 5(x + 2) \).