Question

Find those values of c for which the equations 2x + 3y = 3; (c + 2)x + (c + 4)y = (c + 6) and (c + 2)²x + (c + 4)²y = (c + 6)² are consistent. Also solve the equations for those values of c

Answer 1

The condition for consistency is

For c = 0, the three equations are

2x + 2y = 3; 2x + 4y = 6; 4x + 16y = 36

and the solution is x = -3; y = 3.

For c = -10, the equations are

2x + 3y = 3 

 - 8x - 6y = -4 ⇒ 4x + 3y = 2

64x - 36y = 16 ⇒ 16x + 9y = 4

and the corresponding solution is x= 1/2,;y = 4/3.