[SoLiDUS]

As promised, the solutions to my problems

[code:593bc]

X X Y 40

Z Y Z 50

X Y Z ?

35 50 50
[/code:593bc]

Solution:

(X+Y+Y) + (Y+Z+Z) + (X+Z+X) - (X+X+Y) - (Y+Z+Z) = X + Y + Z

( (X+Y+Y) + (Y+Z+Z) + (X+Z+X) ) - ( (X+X+Y) - (Y+Z+Z) ) = X + Y + Z

( 50 + 50 + 35 ) - ( 40 + 50 ) = 135 - 90 = 45


[code:593bc]

X X Y Z ?

X W Y W 85

Z Y X Z 87

W X Y Z 82

87 86 93 79
[/code:593bc]

Solution:

Use line worth 79 and solve w = 79 - 3z

2x + (79 - 3z) + z = 87
2x + 79 - 2z = 87
2x - 2z = 8
2x - 8 = 2z
Solve for z = x - 4

2 (x - 4) + x + y = 87
2x -8 + x + y = 87
3x + y = 95
Solve for y = 95 - 3x

3y + x = 93
3 (95 - 3x) + x = 93
285 - 8x = 93
192 = 8x
Solve for x = 24

Since z = x - 4,
Solve z = 24 - 4 = 20

Since y = 95 - 3x,
Solve y = 95 - 3(24) = 95 - 72 = 23

Since we know X, Y and Z, we can solve the first line:
24 + 24 + 23 + 20 = 91