proportion

Find the ratio of x:y:z from the following equations:

ax + by + cz = 0
lx + my + nz = 0



Answer

divide the 2 equations by z, we get,

a(x/z) + b(y/z) + c = 0

l(x/z) + m(y/z)+ n = 0

write as follows:

b                c               a             b

m               n                l             m   

cross multiply:
x/z = (bn - mc)/ (am - lb)


y/z = (cl - na) / (am - bl)


So, x/ (bn - mc) = y/ (cl - na) = z/ (am - lb)  answer