Consider the linear system

We can eliminate x from the second equation by adding -2 times the first equation to second. This yields the simplified system

The second equation does not any retrictions on x and y and hence can be omitted. Thus, the solutions of system are those values of x and y that satisfy the single equations 2x – 4y = 1. Geometrically, this means the lines correspoding to the two equations in the original system coincide which gives us that the system has infinitely many solutions.

Solving the equations 2x – 4y = 1 for x in terms of y gives us that x = 2x + 1/2. Assigning an arbitrary value t to y we can express the solutions fo the system in terms of the parametric equations x = 2t + 1/2 and y = t.

Hence (2t + 1/2, t) is a solution of the system above for all

Here’s a sketch of the line 2x – 4y = 1