Which of the following equations have infinitely many solutions?
(Choice A) A -10x-10=-10x-10−10x−10=−10x−10
(Choice B) B 10x-10=-10x+1010x−10=−10x+1010,
(Choice C) C 10x-10=-10x-1010x−10=−10x−1010,
(Choice D) D -10x-10=-10x+10−10x−10=−10x+10

Choice A

Step-by-step explanation:

In each case, each equation has an equation of a line in y = mx + b form equaling another equation of a line in y = mx + b form. If the two sides are equal, it is the same equation, there are infinitely many solutions. If the sides are different, then if the slopes are different, the lines intersect at one point, and there is exactly 1 solution. If the slopes are equal, the lines are parallel, and there is no solution.

(Choice A) -10x-10=-10x-10

In Choice A, both sides of the equation are equal, so there are infinitely many solutions.

(Choice B) 10x-10=-10x+10

(Choice C) 10x-10=-10x-10

(Choice D) -10x-10=-10x+10

In choices B through D, the two sides are not equal, so there is either 1 solution (B and C since they have different slopes) or no solution (D since the slopes are equal).