Question

Verify that the following pair of equations has a unique solution and find the
solution: ax + by + p = 0, ax − cy − q = 0

Answer 1

Answer:

ax+by = -p

ax = - by - p

x = -(b+p) /a

now putting the value of x in the following

ax - cy = q

a*-(b+p) /a - cy = q

-(b+p) - cy = q

multiplying by -1 both sides

b+p+cy = -q

cy = - q - b - p

cy = -(b+p+q)

y = - (b+p+q) /c

hence,

x = -(b+p) /a ; y = - (b+p+q) /c