Question

Solve this equation from elimination method :- ax + by + c = 0; bx + ay + b = 0

Answer 1

1) ax+by+c=0
2) bx+ay+b=0

Multiplying 1) and 2) by b and a respectively.
  abx+b²y+ac=0
  abx+a²y+ab=0
  -     -      -
Subtracting
(b²-a²)y+a(c-b)=0
(b²-a²)y=-a(c-b)
y=-a(c-b)/b²-a²←

Substitiuting in 1)
ax+b[-a(c-b)/b²-a²]=0
ax+[-ab(c-b)/b²-a²]=0
ax=-[-ab(c-b)/b²-a²]=0
ax=ab(c-b)/b²-a²
x=b(c-b)/b²-a²