Solve a 2×2 system
Guided practice — solve each problem, check, then generate a fresh one.
Formula to apply
a x + b y = e c x + d y = f
Problem
Solve the system:
2x + 3y = 13
1x + 2y = 8
Working
- 1det = a·d − b·c = 2·2 − 3·(1) = 1.
- 2x = (e·d − b·f)/det = (13·2 − 3·8)/1 = 2.
- 3y = (a·f − e·c)/det = (2·8 − 13·(1))/1 = 3.