Question 360039
Ax + By = 3
  
a) x = 8, y = 3, plugged in the equation : 8A + 3B = 3
 
b) x = 13, y = 7 gives the equation : 13A + 7B = 3
 
 
equ 7(a)-3(b) eliminates the B : 7*8A-3*13A = 7*3 - 3*3 
 
 (56 - 39)A = 21 - 9
 
 17A = 12
 
 A = 12 / 17 (a)=> B = (3 - 8*12/17)/3 = (51 - 96)/17/3 = -45/17/3 = -15 / 17
  
 (b)=> B = (3 - 13*12/17)/7 = (51 - 156)/17/7 = -105/17/7 = -15 / 17
 
 
the equation is : 3/17(4x-5y) = 3
 
4x - 5y = 17
 
 
 
Verification : 
 
3/17*(4*8 - 5*3) = 3/17*(32 - 15) = 3/17*17 = 3
 
3/17*(4*13 - 5*7) = 3/17*(52 - 35) = 3/17*17 = 3