The two-by-two linear system
ax + by = e,
cx + dy = f ,
Where a, b, c, d, e, f are given, can be solved for x and y as follows:
Set m = c/a, provided a ≠ 0;
d1 = d − mb;
f1 = f − me;
y = f1/d1;
x = (e − by)/a
Solve the following linear systems using four-digit rounding arithmetic.
a. 1.130x − 6.990y = 14.20
1.013x − 6.099y = 14.22
b. 8.110x + 12.20y = −0.1370
−18.11x + 112.2y = −0.1376