give an example if a linear equation in one variable with infinitely many solutioms. Explain how you know it has many solutions.

Ask expert and try to use your brain and why do you want to know many solutions just study one that's enough

There can be zero solutions, 1 solution or infinite solutions--each case is explained in detail below. Note: Although systems of linear equations can have 3 or more equations, we are going to refer to the most common case--a stem with exactly 2 lines. Case I: 1 Solution

This is the most common situation and it involves lines that intersect exactly 1 time.

Case 2: No Solutions

This only happens when the lines are parallel. As you can see, parallel lines are not going to ever meet.

Example of a stem that has no solution:

Line 1: y = 5x + 13 Line 2: y = 5x + 12

Case 3: Infinite Solutions

This is the rarest case and only occurs when you have the same line

Consider, for instance, the two lines below (y = 2x+1 and 2y = 4x + 2). These two equations are really the same line.

Example of a system that has infinite solutions:

Line 1: y = 2x + 1 Line 2: 2y = 4x + 2