If the straight line ax + by + c = 0 passes through the point (1,1) then solve the following system of equations:

bcx + cay = a³ + b³ + c ³

and 2x + 2y = 3(a+b).

Question

If the straight line ax + by + c = 0
passes through the point (1,1) then solve the following system of
equations:
bcx + cay = a3 + b3 +
c 3
and 2x + 2y = 3(a+b)

Abhishek Kr. Jha · Accepted Answer

Since the straight line ax+by+c = 0 passes through the point (1, 1)
then we have;
a1+b1+c = 0⇒a+b+c = 0⇒a+b+c3 = 0 {cubing on both
sides}⇒a3+b3+c3+3ab+bc+ac = 0 ⇒a3+b3+c3 = -3ab+bc+ac
(i)
Now the given system of equations are;
bcx+cay = a3+b3+c3⇒bcx+cay = -3ab+bc+ac (ii) {using (i)}2x+2y
= 3a+b (iii)Multiplying (ii) by 2 and (iii) by bc and then
subtracting (iii) from (ii) we get;2bcx+2cay-2bcx-2bcy =
-6ab+bc+ac-3bca+b⇒2cya-b = -6ab+bc+ac-3bca+b⇒y =
-6ab+bc+ac-3bca+b2ca-bThen from (iii) we
have;2x+2-6ab+bc+ac-3bca+b2ca-b =
3a+b⇒2x-6ab+bc+ac+3bca+bca-b = 3a+b⇒2x =
3a+b+6ab+bc+ac+3bca+bca-b⇒x = 32a+b+6ab+bc+ac+3bca+b2ca-b
(answer)

If the straight line ax + by + c = 0 passes through the point (1,1) then solve the following system of equations: bcx + cay = a3 + b3 + c 3 and 2x + 2y = 3(a+b).

If the straight line ax + by + c = 0 passes through the point (1,1) then solve the following system of equations:

bcx + cay = a³ + b³ + c ³

and 2x + 2y = 3(a+b).