Question 88885
  Solve by any convenient method : 
4x + 12y = 24                         1)4x+12y = 24 ..........eq'n(1)
2x + 6y = 12                             2x+6y = 12...........eq'n(2) 
                                         divide eq'n (1) by 4 andeq'n (2) by 2
                                        we get x+3y = 6    and x+3y =6
                           there is no solution for this set of eq'ns as the 
       given eq'ns are inconsistent. (on solving the values of x & y are 0 which is meaningless)






Solve by any convenient method :   8x+4y = 7..........(1)
8x + 4y =7
x = 2-2y                           x+2y = 2............(2)

Solve by Elimination :             multiply  eq'n (2) by 2
2x -3y =-1
3x + y +15                         we get 2x+4y = 4.........eqe'n(3)

Solve by Substitution :            subtract eq'n(3) from eq'n(1)  we get 
3x + 8y = 7
x- 4y =9                           6x = 3    or x = 3/6 = 1/2
                                  substitute  for x  in eq'n(2)
                                   2y = 2-x  = 2-1/2 = 4-1/2 = 3/2
                                   solution  is x= 1/2  and y = 3/2




                               3)2x-3y = -1......eq'n(1)

                                 3x+y  = 15......eq'n(2)
                                multiply eq'n(2)  by 3, we get 9x+3y = 45....(3)
                              add eq''n(1) &eq'n(3) we get 11x = 44   or x = 4
                               substitute for x in eq'n (2) we get 3(4)+y= 15

                                          12+y = 15  or y = 15-12 = 3

                          solution  is x = 4  and y = 3





                           4)3x+8y = 7.........eq'n(1)
                             x-4y  = 9.........eq'n(2)
                     from  eq'n(2) x = 9+4y.....eq'n(3)
                            3(9+4y)+8y = 7     (by substituting for x)
                            27+12y+8y  = 7
                              20y   =  7-27 = -20 therefore y = -1

                             substituting for y in eq'n(2)  we get x = 9+4(-1)
                                   x = 9-4 = 5

      therefore the solution  is x = 5  and y = -1