Solve the system.
-$\left\{ \begin{array} { r r }
x + y & = - 3 \
- 5 x - 5 y + 5 z & = 35 \
x - z & = - 8
\end{array} \right.$
A) $( - 4,1,4 )$
B) $( 4,1 , - 4 )$
C) $( 4 , - 4,1 )$
D) $( - 4,4,1 )$

Question

Solve the system.
-$\left\{ \begin{array} { r r } 
x + y & = - 3 \
- 5 x - 5 y + 5 z & = 35 \
x - z & = - 8
\end{array} \right.$
A) $( - 4,1,4 )$
B) $( 4,1 , - 4 )$
C) $( 4 , - 4,1 )$
D) $( - 4,4,1 )$

Quizplus · Accepted Answer

Solving the system of equations, we start by adding the first and third equations to eliminate $z$, leading to $2x = -11$, which gives $x = -\frac{11}{2}$, not matching any of the options. However, if we directly substitute $x = -4$ from option A into the first equation, we get $y = 1$, and substituting $x = -4$ and $y = 1$ into the second equation gives $z = 4$, confirming option A as correct.

Solve the System {x+y=−3−5x−5y+5z=35x−z=−8\left\{ \begin{array} { r r } x + y & = - 3 \\- 5 x - 5 y + 5 z & = 35 \\x - z & = - 8\end{array} \right.⎩⎨⎧​x+y−5x−5y+5zx−z​=−3=35=−8​

Solve the System $\left\{ \begin{array} { r r } x + y & = - 3 \\- 5 x - 5 y + 5 z & = 35 \\x - z & = - 8\end{array} \right.$