Solve the system.
-$$\begin{array} { l }
6 x + 6 y - z = 32 \
x + 9 y - 4 z = - 2 \
6 x + y + z = 35
\end{array}$$
A) $\{ ( 5,1,4 ) \}$
B) $\{ ( - 5,1,10 ) \}$
C) $\varnothing$
D) $\{ ( 5,4,1 ) \}$

Question

Solve the system.
-$$\begin{array} { l } 
6 x + 6 y - z = 32 \
x + 9 y - 4 z = - 2 \
6 x + y + z = 35
\end{array}$$
A) $\{ ( 5,1,4 ) \}$
B) $\{ ( - 5,1,10 ) \}$
C) $\varnothing$
D) $\{ ( 5,4,1 ) \}$

Quizplus · Accepted Answer

To solve the system of equations, you can use methods such as substitution, elimination, or matrix operations. Here, we can quickly use elimination to simplify and solve:1. Subtract the third equation from the first to eliminate $x$ and $y$, getting an equation in $z$.2. Use the second equation to express $x$ in terms of $y$ and $z$, then substitute into one of the other equations to solve for $y$ and $z$.3. Once $y$ and $z$ are found, substitute back to find $x$.Following these steps or directly solving using a matrix approach will lead to the solution $(5, 1, 4)$, which matches choice A.

Solve the System 6x+6y−z=32x+9y−4z=−26x+y+z=35\begin{array} { l } 6 x + 6 y - z = 32 \\x + 9 y - 4 z = - 2 \\6 x + y + z = 35\end{array}6x+6y−z=32x+9y−4z=−26x+y+z=35​

Solve the System $\begin{array} { l } 6 x + 6 y - z = 32 \\x + 9 y - 4 z = - 2 \\6 x + y + z = 35\end{array}$