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 = 7
1x + 2y = 5
Working
- 1det = a·d − b·c = 2·2 − 3·(1) = 1.
- 2x = (e·d − b·f)/det = (7·2 − 3·5)/1 = -1.
- 3y = (a·f − e·c)/det = (2·5 − 7·(1))/1 = 3.