Solve the system. $\left\{ \begin{array} { l }
x + y + z = 4 \
x - y + z = 0 \
x - y - z = 6
\end{array} \right.$
A) $( 4,2 , - 3 )$
B) $( 5,2 , - 3 )$
C) $( - 5,2 , - 3 )$
D) The system is inconsistent.
E) The equations are dependent.

Question

Solve the system. $\left\{ \begin{array} { l } 
x + y + z = 4 \
x - y + z = 0 \
x - y - z = 6
\end{array} \right.$
A) $( 4,2 , - 3 )$
B) $( 5,2 , - 3 )$
C) $( - 5,2 , - 3 )$
D) The system is inconsistent.
E) The equations are dependent.

Quizplus · Accepted Answer

To solve the system, we can add the second and third equations to eliminate $z$, giving $2x - 2y = 6$, which simplifies to $x - y = 3$. Adding the first and third equations gives $2x + 0y = 10$, or $x = 5$. Substituting $x = 5$ into $x - y = 3$ gives $y = 2$. Finally, substituting $x = 5$ and $y = 2$ into any of the original equations, for example, the first one, gives $z = -3$. Therefore, the solution is $(5, 2, -3)$.

Solve the System {x+y+z=4x−y+z=0x−y−z=6\left\{ \begin{array} { l } x + y + z = 4 \\x - y + z = 0 \\x - y - z = 6\end{array} \right.⎩⎨⎧​x+y+z=4x−y+z=0x−y−z=6​

Solve the System $\left\{ \begin{array} { l } x + y + z = 4 \\x - y + z = 0 \\x - y - z = 6\end{array} \right.$