( 1 ) 3 x + 3 y + 6 z = 3 ( 2 ) 3 x + 2 y + 6 z = 7 ( 3 ) 4 x + 4 y + 7 z = 4 ( 1 ) − ( 2 ) ⇒ 3 x + 3 y + 6 z − ( 3 x + 2 y + 6 z ) = 3 − 7 3 x + 3 y + 6 z − 3 x − 2 y − 6 z = − 4 y = − 4 4 ⋅ ( 1 ) − 3 ⋅ ( 3 ) ⇒ 4 ⋅ ( 3 x + 3 y + 6 z ) − 3 ⋅ ( 4 x + 4 y + 7 z ) = 4 ⋅ 3 − 3 ⋅ 4 12 x + 12 y + 24 z − 12 x − 12 y − 21 z = 12 − 12 3 z = 0 / : 3 z = 0
( 1 ) 3 x + 3 y + 6 z = 3 / : 3 x + y + 2 z = 1 y = − 4 an d z = 0 ⇒ x − 4 + 2 ⋅ 0 = 1 ⇒ x = 1 + 4 ⇒ x = 5 A n s . x = 5 , y = − 4 , z = 0
The solution for the system of equations is x = 5, y = -4, and z = 0. We derived this by simplifying the equations step-by-step and substituting the derived values back into the original equations. This method allows us to find the values of the variables accurately.
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