Solve the system in terms of the arbitrary variable x.
-$$\begin{array} { r }
x + y + z = 9 \
4 x - 3 y + 2 z = 7
\end{array}$$

A) $\left. \left\{ x , \frac { 2 x - 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$
B) $\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$
C) $\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { x + 34 } { 5 } \right) \right\}$
D) $\varnothing$

Question

Solve the system in terms of the arbitrary variable x.
-$$\begin{array} { r } 
x + y + z = 9 \
4 x - 3 y + 2 z = 7
\end{array}$$

A) $\left. \left\{ x , \frac { 2 x - 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$
B) $\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$
C) $\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { x + 34 } { 5 } \right) \right\}$
D) $\varnothing$

Quizplus · Accepted Answer

To solve the system in terms of $x$, we can express $y$ and $z$ as functions of $x$. Subtracting the first equation from the second (multiplied by an appropriate factor to eliminate $z$) or using substitution methods will lead to expressions for $y$ and $z$ in terms of $x$. The correct expressions for $y$ and $z$ are $\frac{2x+11}{5}$ and $\frac{-7x+34}{5}$, respectively, which matches option B.

Solve the System in Terms of the Arbitrary Variable X x+y+z=94x−3y+2z=7\begin{array} { r } x + y + z = 9 \\4 x - 3 y + 2 z = 7\end{array}x+y+z=94x−3y+2z=7​

Solve the System in Terms of the Arbitrary Variable X $\begin{array} { r } x + y + z = 9 \\4 x - 3 y + 2 z = 7\end{array}$