Indeterminate system

Imagine you're building a tower out of blocks, but you don't know how many blocks you have. You start stacking them up but you're never sure when you'll run out, so you just keep adding more and more blocks until you have a really tall tower. This is kind of like an indeterminate system in math.

An indeterminate system is one where you have more unknowns (things you don't know) than equations (things you do know). It's like trying to solve a puzzle with missing pieces. You might be able to guess what some of the missing pieces are, but you'll never really know for sure.

For example, let's say you have two equations:

3x + 4y = 10

2x - y = 1

This system is determinate because you have two equations and two unknowns (x and y). You can solve for x and y and find out exactly what they are.

But let's say you have three equations:

x + y + z = 6

2x - y + 3z = 10

3x + y - 2z = 2

This system is indeterminate because you have three unknowns (x, y, and z) but only three equations. You can solve for one of the variables in terms of the other two, but you'll still have an infinite number of solutions because there are more unknowns than equations.

So an indeterminate system is like a puzzle with missing pieces that you can't really solve completely. It's a bit like stacking blocks without knowing how many you have - you can keep adding more and more, but you'll never really be sure if you've got it right.