Solve the system of linear equations below. { 2 x + 3 y = − 18 z = 4 x − 8 y − z = 6 \left\{ \begin{aligned}2 x + 3 y & = - 18 \z & = 4 \x - 8 y - z & = 6\end{aligned} ight. ⎩ ⎨ ⎧ 2 x + 3 y z x − 8 y − z = − 18 = 4 = 6 A) ( 4 , − 6 , − 2 ) ( 4 , - 6 , - 2 ) ( 4 , − 6 , − 2 ) B) ( − 6 , 4 , − 2 ) ( - 6,4 , - 2 ) ( − 6 , 4 , − 2 ) C) ( − 2 , 4 , − 6 ) ( - 2,4 , - 6 ) ( − 2 , 4 , − 6 ) D) ( 4 , 0 , 1 ) ( 4,0,1 ) ( 4 , 0 , 1 ) E) ( − 6 , − 2 , 4 ) ( - 6 , - 2,4 ) ( − 6 , − 2 , 4 )

Question

Solve the system of linear equations below.   { 2 x + 3 y = − 18 z = 4 x − 8 y − z = 6 \left\{ \begin{aligned}2 x + 3 y  &  = - 18 \z  &  = 4 \x - 8 y - z  &  = 6\end{aligned} ight. ⎩ ⎨ ⎧ ​ 2 x + 3 y z x − 8 y − z ​ = − 18 = 4 = 6 ​ A)    ( 4 , − 6 , − 2 )  ( 4 , - 6 , - 2 )  ( 4 , − 6 , − 2 )  B)    ( − 6 , 4 , − 2 )  ( - 6,4 , - 2 )  ( − 6 , 4 , − 2 )  C)    ( − 2 , 4 , − 6 )  ( - 2,4 , - 6 )  ( − 2 , 4 , − 6 )  D)    ( 4 , 0 , 1 )  ( 4,0,1 )  ( 4 , 0 , 1 )  E)    ( − 6 , − 2 , 4 )  ( - 6 , - 2,4 )  ( − 6 , − 2 , 4 )

Jesus Marquez · Accepted Answer

Final Answer : E, Explanation :   Given   z = 4 z = 4 z = 4  , substitute   z z z   into the third equation:   x − 8 y − 4 = 6 x - 8y - 4 = 6 x − 8 y − 4 = 6  , which simplifies to   x − 8 y = 10 x - 8y = 10 x − 8 y = 10  . Now, we have two equations in   x x x   and   y y y  :   2 x + 3 y = − 18 2x + 3y = -18 2 x + 3 y = − 18   and   x − 8 y = 10 x - 8y = 10 x − 8 y = 10  . Solving this system of equations yields   x = − 6 x = -6 x = − 6   and   y = − 2 y = -2 y = − 2  , with   z z z   already given as   4 4 4  . Therefore, the solution is   ( − 6 , − 2 , 4 ) (-6, -2, 4) ( − 6 , − 2 , 4 )  .

Solve the system of linear equations below. ${2x+3y=−18z=4x−8y−z=6\left\{ \begin{aligned}2 x + 3 y & = - 18 \\z & = 4 \\x - 8 y - z & = 6\end{aligned} \right.$

A) $(4, - 6, - 2)$
B) $(- 6, 4, - 2)$
C) $(- 2, 4, - 6)$
D) $(4, 0, 1)$
E) $(- 6, - 2, 4)$

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