Three equations
Three equations are given above, what is the value of ?
The answer is 0.
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1 solution
Given that,
3 x + 2 y − 4 z = 4 . . . . . . . . . . . . . . . ( 1 )
− 2 x + 3 y + z = 1 2 . . . . . . . . . . . . . . . ( 2 )
x − 2 y + 2 z = − 1 0 . . . . . . . . . . . . . ( 3 )
Now, Multiply equation (2) by 4 and equation (3) by 2.
3 x + 2 y − 4 z = 4 . . . . . . . . . . . . ( 1 )
− 8 x + 1 2 y + 4 z = 4 8 . . . . . . . ( 4 ) )
2 x − 4 y + 4 z = − 2 0 . . . . . . . . ( 5 ) )
Add equations (1) and (4). ⇒ − 5 x + 1 4 y = 5 2 . . . . . . ( 6 )
Add equations (1) and (5). ⇒ 5 x − 2 y = − 1 6 . . . . . . . . . . . ( 7 )
Add equations (6) and (7). ⇒ 1 2 y = 3 6 ⇒ y = 3
Now we have the value of y .
Substitute the value of y back into equation (7) to find x
5 x − 6 = − 1 6
⇒ 5 x = − 1 0 ⇒ x = − 2
Now we have the values of y and x .
Substitute these values back into equation (2) to find z .
⇒ 4 + 9 + z = 1 2 ⇒ z = − 1
Therefore, ⇒ x + y + z = − 2 + 3 + ( − 1 ) = 0 .