Question

Which graph below shows a system of equations with infinitely many solutions?

A)coordinate plane with two parallel lines
B)coordinate plane with two intersecting lines
C)coordinate plane with two coinciding lines
D)coordinate plane with two intersecting lines

Answer 1

That would be a coordinate plane with two coinciding lines. Coinciding lines are two lines laying one on top of the other. Same line, infinite solutions.

Answer 2

Answer: C)coordinate plane with two coinciding lines has infinitely many solution.

Explanation:

Since, By option A) If there is a coordinate plane with two parallel lines.

Then, It has no solution ( because, we get the solution at the the intersection point of the two lines but parallel lines do not intersect each other).So, it does not have infinite many solution.

By Option B) If there are two intersecting lines then we can get only one solution. So, it does not have infinite many solution.

By Option C) If there are two coinciding lines then we can get infinite number of intersection points therefore the system must have infinite number of solution.

Note: here, Option D) is same as Option B)

Therefore Only option C) is correct.