Solve the system. $\left\{ \begin{array} { l }
x + y + z = 5 \
2 x + y - z = 5 \
2 x - 3 y + z = - 1
\end{array} \right.$
A) $( - 3 , - 1,1 )$
B) $( 2 , - 2 , - 1 )$
C) $( 2,2,1 )$
D) The equations are dependent.
E) The system is inconsistent.

Question

Solve the system. $\left\{ \begin{array} { l } 
x + y + z = 5 \
2 x + y - z = 5 \
2 x - 3 y + z = - 1
\end{array} \right.$
A) $( - 3 , - 1,1 )$
B) $( 2 , - 2 , - 1 )$
C) $( 2,2,1 )$
D) The equations are dependent.
E) The system is inconsistent.

Quizplus · Accepted Answer

We can solve this system using elimination or substitution. Using elimination, we can add the first and second equations to eliminate y: 
$$3x=10 \Rightarrow x= \frac{10}{3}$$ 
Substituting this into the first equation yields: $$\frac{10}{3}+y+z=5 \Rightarrow y+z=\frac{5}{3}$$ 
Next, we can add the second and third equations to eliminate z: 
$$4x-2y=-6 \Rightarrow 2x-y=-3$$ 
$$2x-y=-3 $$
Now, we can solve for y: 
$$y=2x+3$$ 
Substituting this equation into $y+z=\frac{5}{3}$ gives: 
$$2x+3+z=\frac{5}{3} \Rightarrow z = \frac{-1}{3} $$

Therefore, the solution is $(2,2,1)$, which corresponds to choice C.

Solve the System {x+y+z=52x+y−z=52x−3y+z=−1\left\{ \begin{array} { l } x + y + z = 5 \\2 x + y - z = 5 \\2 x - 3 y + z = - 1\end{array} \right.⎩⎨⎧​x+y+z=52x+y−z=52x−3y+z=−1​

Solve the System $\left\{ \begin{array} { l } x + y + z = 5 \\2 x + y - z = 5 \\2 x - 3 y + z = - 1\end{array} \right.$