Lutasin ang sumusunod na dalawang linear equation sa pamamagitan ng pagpapalit at pag-aalis ng paraan: ax + by = (a-b), bx-ay = (a-b)?

Sagot:

# x = (a ^ 2-b ^ 2) / (a ^ 2 + b ^ 2) # at # y = (2ab-a ^ 2-b ^ 2) / (a ^ 2 + b ^ 2) #

# a * (ax + by) + b * (bx-ay) = a * (a-b) + b * (a-b) #

# a ^ 2 * x + aby + b ^ 2 * x-aby = a ^ 2-ab + ab-b ^ 2 #

# (a ^ 2 + b ^ 2) * x = a ^ 2-b ^ 2 #

# x = (a ^ 2-b ^ 2) / (a ^ 2 + b ^ 2) #

Kaya, # a * (a ^ 2-b ^ 2) / (a ^ 2 + b ^ 2) + ng = a-b #

# a * (a ^ 2-b ^ 2) + ng * (a ^ 2 + b ^ 2) = (a-b) * (a ^ 2 + b ^ 2) #

# a ^ 3-ab ^ 2 + (a ^ 2 + b ^ 2) * by = a ^ 3 + ab ^ 2-a ^ 2 * b-b ^ 3 #

# (a ^ 2 + b ^ 2) * by = 2ab ^ 2-a ^ 2 * b-b ^ 3 #

# y = (2ab ^ 2-a ^ 2 * b-b ^ 3) / b * (a ^ 2 + b ^ 2) #

=# (2ab-a ^ 2-b ^ 2) / (a ^ 2 + b ^ 2) #