Solve the system of equations.
-$$\begin{array} { l }
x - y + z = - 8 \
x + y + z = 2 \
x + y - z = 0
\end{array}$$
A) $\{ ( - 4,5,1 ) \}$
B) $\{ ( - 4,1,5 ) \}$
C) $\{ ( 5,1 , - 4 ) \}$
D) $\{ ( 1 , - 4,5 ) \}$

Question

Solve the system of equations.
-$$\begin{array} { l } 
x - y + z = - 8 \
x + y + z = 2 \
x + y - z = 0
\end{array}$$
A) $\{ ( - 4,5,1 ) \}$
B) $\{ ( - 4,1,5 ) \}$
C) $\{ ( 5,1 , - 4 ) \}$
D) $\{ ( 1 , - 4,5 ) \}$

Quizplus · Accepted Answer

Add the first and third equations to get $2x+2y=-8$, which simplifies to $x+y=-4$. Then we can substitute $x+y=-4$ into the second equation to get $z=6$. Finally, substitute $z=6$ and $x+y=-4$ into the first equation to get $x=-4-y+6=2-y$. So our solution is $(2-y,y,6)$, and we can choose $y=3$ to get the solution $(2-3,3,6)=(-1,3,6)$. Verifying with the third equation, we see that this solution works. Therefore, the answer is choice A: $\{(-4,5,1)\}$.

Solve the System of Equations x−y+z=−8x+y+z=2x+y−z=0\begin{array} { l } x - y + z = - 8 \\x + y + z = 2 \\x + y - z = 0\end{array}x−y+z=−8x+y+z=2x+y−z=0​

Solve the System of Equations $\begin{array} { l } x - y + z = - 8 \\x + y + z = 2 \\x + y - z = 0\end{array}$