Question 2236
First of all I am solving the 2nd problem.

  7x+3Y=14      ......   (1)
  5x+9y=10      ......   (2)
By multiplying (1) by 3, we get,
  21x+9y=42     ......   (3)
Eq.(3)-(2), we get,
  16x = 32
=   x = 32/16 = 2
Now, replacing the value of x in (1), we get
=  7*2 + 3y = 14
=  14 + 3y = 14
=  3y =14-14=0
so, y = 0
  x=2; y=0;  Ans.

Now take the last problem. 

  12x+y=25   ............(1)
   8x-2y=14  ............(2)
  24x+2y=50  ............(3) (By multiplying (1) by 2)
(3)+(2), we get
  32x = 64
So x = 64/32 = 2
Now, replacing the value of x in (2), we get
  8*2 - 2y = 14
=16 - 2y = 14
=2y =16-14 = 2
so y = 2/2 = 1

x=2; y=1;  Ans.

Why I have solved  only two problems is, you should also try to solve.
First, try to eliminate one variable either by adding or by subtracting.  If a variable is not same in both the equations, then, make the variable of one equation equal to that of another either by multiplying or by dividing the equation so that we can eliminate one variable as stated earlier in the para.
Understood !  C'mon solve the other problems.