2x+2y=7 ( 1)

6(x+y)-4x=33 is simplified to 2x+6y=33 (2).

(2)-( 1)，4y=26 ∴y=6.5.

Substitute (1) to get x=-3.

2、

x+y=3

X-y= 1 gives x = 2 and y= 1.

Substitute x-my=2 and nx-y=2, and you get

2-m=2，2n- 1=2

The solution is m = 0 and n = 3/2.

3、

3x+2y=4k+3 ( 1)

2x+y=2k+ 1 (2)

( 1)-(2) x+y=2k+2。

Because the satisfactory solution x+y=6

So 2k+2=6.

∴ k=2

4、

4(x- 1)-5(y+ 1)=29 is simplified to 4x-5y=38 (1).

Three-thirds x+ three-quarters y= half, which is simplified as 4x+3y=6 (2).

(2)-( 1) 8y=-32 ∴y=-4.

Substitution into (2) gives x=4.5.

5、

2x+my=4 ( 1)

Simplify X-2y=0 and get x=2y.

Substitute (1) to get 4y+my=4.

∴y=4/(m+4) x=8/(m+4)

Because the solution of the equation is a positive integer

So m+4= 1 or 2 or 4.

M=-3 or m=-2 or m=0.

Because m takes a non-negative integer

So m=0