Question

How do you solve the system of equations `2x - 5y = 10` and `4x - 10y = 20`?

Answer 1

There are an infinite number of solutions for this pair of equations since they are just two different versions of the same line.

If you re-write `2x-5y = 10` as a linear (that means in a form that can be drawn as a straight line) function in standard format, you would get `y = (2x-10)/5`. If you re-write `4x-10y=20` as a function in standard form you would also get `y = (2x-10)/5`. Therefore both equations represent the same line; any (x,y) pair that works for one also works for the other.

If you have two linear equations (which you can think of as two straight lines drawn in the xy-plane) there are 3 possibilities: they cross at exactly one point; they don't cross (that is they are parallel like train tracks); or they are exactly the same line so they match up at every point along the line.