Solve Systems of Linear Equations in Three Variables
-$$\begin{array} { c }
x + y + z = - 7 \
x - y + 3 z = - 13 \
2 x + y + z = - 9
\end{array}$$
A) $\{ ( - 2 , - 1 , - 4 ) \}$
B) $\{ ( - 1 , - 2 , - 4 ) \}$
C) $\{ ( - 4 , - 1 , - 2 ) \}$
D) $\{ ( - 4 , - 2 , - 1 ) \}$

Question

Solve Systems of Linear Equations in Three Variables
-$$\begin{array} { c } 
x + y + z = - 7 \
x - y + 3 z = - 13 \
2 x + y + z = - 9
\end{array}$$
A) $\{ ( - 2 , - 1 , - 4 ) \}$
B) $\{ ( - 1 , - 2 , - 4 ) \}$
C) $\{ ( - 4 , - 1 , - 2 ) \}$
D) $\{ ( - 4 , - 2 , - 1 ) \}$

Quizplus · Accepted Answer

To solve the system of equations, you can use methods such as substitution or elimination. By subtracting the first equation from the third, you can eliminate $y$, leading to an equation in $x$ and $z$. Similarly, you can eliminate $y$ from the first two equations to find another equation in $x$ and $z$. Solving these two new equations will give you the values of $x$ and $z$, and substituting these values back into one of the original equations will give you $y$. The solution that fits all three equations is $(-2, -1, -4)$.

Solve Systems of Linear Equations in Three Variables - x+y+z=−7x−y+3z=−132x+y+z=−9\begin{array} { c } x + y + z = - 7 \\x - y + 3 z = - 13 \\2 x + y + z = - 9\end{array}x+y+z=−7x−y+3z=−132x+y+z=−9​

Solve Systems of Linear Equations in Three Variables
- $\begin{array} { c } x + y + z = - 7 \\x - y + 3 z = - 13 \\2 x + y + z = - 9\end{array}$