ELI5: one equation with two unknowns has infinitely many answers — but two equations pin down a single (x, y). Elimination is the cleanest by-hand method: line the equations up so that adding them makes one variable vanish.
Solve 2x + y = 8 and x − y = 1: add them and the y's cancel → 3x = 9 → x = 3, then back-substitute for y = 2.
xs=38+1 = 3 add the equations: (2x + y) + (x − y) = 9 ys=xs−1 = 2 back-substitute into x − y = 1 ✓ pass abs(2⋅xs+ys−8)<10−9 first equation holds ✓ pass abs(xs−ys−1)<10−9 second equation holds Elimination by hand is the understanding; solveSystem is the shortcut — give it the equations, the variable you want, and the list of unknowns.
xsys:=solveSystem(["2∗x+y=8","x−y=1"],"x",["x","y"]) = 3 the engine solves the pair for x ✓ pass xsys==xs matches the elimination by hand Real-world hook: systems are everywhere two quantities trade off — mixing two coffee blends to a target price, splitting a trip between two speeds, balancing supply and demand.
Try it yourself: solve x + y = 7 and 2x − y = 8 for x. (Add the equations: the y's cancel.)
xyou=5 ✏️ Your turn: solve the system for x. The check substitutes y = 2x − 8 (from the 2nd equation) into x + y = 7 — so you must find the real x. ✓ pass abs(xyou+2⋅xyou−8−7)<10−9 green when your x satisfies both equations