Is it a separate question to ask “is a system solvable” vice “is an equation solvable”? and does that change if the equation is part of the system in question?
On prepswift, the system of equations quiz and the “Are 2-Variable Equations Solvable?” lesson notes seem to conflict. I’m not finding it clear if these are two separate things or if they are the same thing getting two conflicting explanations.
The quiz (in question 3’s explanation) says a system of equations is solvable when containing only equivalent equations, while the lesson (in the notes below) says a multi-variable equation isn’t solvable when it’s part of a system of equivalent equations.
Is the system of equations below solvable?
Depends on what u define as “solvable”
You have to post the image cuz rn it’s not visible
Thank you for looking over this with me. I’ve attached pictures to this message.
My definition of solvable is GregMat’s I hope. But I’m unsure what solvable is supposed to mean in the contexts I screenshotted.
Yes, the two images certainly seem to contradict each other here.
Anyway, in general, a system of equations is considered “solvable” if it can have either a unique solution or infinite solutions. Conversely, a system is “unsolvable” if no solution exists. That’s generally all you need to know because it’s unlikely you’d be asked to define “solvable” directly.
Rather, it’s more beneficial for you to understand how to classify a system of linear equations as having either a unique solution, infinite solutions, or no solutions.
