Ordered triple are (4,-2,1)
Explanation:
We need to find ordered triple of 2x + 5y - 3z = -5 , 3x + 2y + 7z = 15 and 5x - 4y + 6z = 34
2x + 5y - 3z = -5 -------------------------eqn 1
3x + 2y + 7z = 15 -------------------------eqn 2
5x - 4y + 6z = 34 -------------------------eqn 3
eqn 1 + eqn 2
5x + 7y + 4z = 10 -------------------------eqn 4
eqn 4 - eqn 3
11y - 2z = -24 -------------------------eqn 5
eqn 1 x 3
6x + 15y - 9z = -15 -------------------------eqn 6
eqn 2 x 2
6x + 4y + 14z = 30 -------------------------eqn 7
eqn 7 - eqn 6
-11y + 23z = 45 -------------------------eqn 8
eqn 5 + eqn 8
21 z = 21
z = 1
Substituting in eqn 8
-11y + 23 x 1 = 45
-11 y = 22
y = -2
Substituting in eqn 1
2x + 5 x -2 - 3 x 1 = -5
2x = 8
x = 4
Ordered triple are (4,-2,1)