SOLUTION: If {x=1,y=-1; {x=2,y=2; {x=3,y=c are the solutions to the equation ax+by+2=0, determine the value of c.

From the "given" part we have, substituting the values into equation


 a -  b = = -2    (1)    (substituting  x= 1, y= -1 into equation)
2a + 2b = = -2    (2)    (substituting  x= 2, y=  2 into equation)


Equivalently


2a - 2b = -4      (1')
2a + 2b = -2      (2')

-------------------------------- Add the equations


4a = -4 - 2 = -6  ====>  a =  =  = -1.5


Then from (1)  b = a + 2 = 0.5.


Now we are in position to determine the value of c.

It is  -1.5*3 + 0.5*c + 2 = 0,   or   c =  = 5.


Answer.  c = 5.