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

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

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