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:
4x + 5y = 23
3x + 4y = 18
Working
- 1det = a·d − b·c = 4·4 − 5·(3) = 1.
- 2x = (e·d − b·f)/det = (23·4 − 5·18)/1 = 2.
- 3y = (a·f − e·c)/det = (4·18 − 23·(3))/1 = 3.