3x + 4y + 3z = 5
2x + 2y + 3z = 5
5x + 6y + 7z = 7
<=> 3( 3x + 4y + 3z) = 5.3
6( 2x + 2y + 3z) = 5.6
2( 5x + 6y + 7z ) = 7.2
<=> 9x + 12y + 9z = 15 (1)
12x + 12y + 18z=30 (2)
10x + 12y + 14z = 14 (3)
<=> 3x +9z =15 [ (2) - (1) ]
2x + 4z = 16. [ (2) - (1) ]
<=> 2(3x +9z) = 15.2
3(2x + 4z) = 16.3
<=> 6x+ 18z = 30
6x + 12z = 48
<=> 6z = - 18 => z = -3 and 6x + 18z = 30 so x = [30 - 18.(-3) ] : 6 = 14
We have 2x + 2y + 3z =5 => 2.14 + 2y + 3.(-3) = 5 ==> y = -7
The answer is x = 14, y = -7, z = -3
