independent system
When two clues genuinely tell you different things, together they can pin down an answer exactly. An independent system is a system whose equations carry distinct, non-redundant information — neither is a disguised copy of the other — so together they single out exactly one solution.
For two linear equations in two unknowns, independence means the lines have different slopes; they cross at precisely one point, and that crossing is the unique solution. The equations cooperate without merely repeating each other, which is what lets the system be both consistent and exactly determined.
Be careful to keep two ideas apart. Independent versus dependent is about whether the equations duplicate information (one solution versus infinitely many). Consistent versus inconsistent is about whether any solution exists at all. An independent linear system is always consistent, with exactly one solution — the cleanest, most familiar case.
x + y = 5 and x − y = 1 are independent: their lines have slopes −1 and 1, so they cross at the single point (3, 2). One solution, uniquely determined.
Distinct equations, one sharp answer.