Find the solution or solutions, if any exist, to the system.
-$$\left\{ \begin{array} { l }
x + y + z = 7 \
x - y + 2 z = 7
\end{array} \right.$$
A) infinitely many solutions of the form $x = 7 - \frac { 3 } { 2 } z , y = \frac { 1 } { 2 } z , z = z$
B) infinitely many solutions of the form $x = - 7 - \frac { 3 } { 2 } z , y = \frac { 1 } { 2 } z , z = z$
C) infinitely many solutions of the form $x = - 7 - \frac { 3 } { 2 } z , y = 2 z , z = z$
D) infinitely many solutions of the form $x = 7 - \frac { 3 } { 2 } z , y = 2 z , z = z$

Question

Find the solution or solutions, if any exist, to the system.
-$$\left\{ \begin{array} { l } 
x + y + z = 7 \
x - y + 2 z = 7
\end{array} \right.$$
A) infinitely many solutions of the form $x = 7 - \frac { 3 } { 2 } z , y = \frac { 1 } { 2 } z , z = z$
B) infinitely many solutions of the form $x = - 7 - \frac { 3 } { 2 } z , y = \frac { 1 } { 2 } z , z = z$
C) infinitely many solutions of the form $x = - 7 - \frac { 3 } { 2 } z , y = 2 z , z = z$
D) infinitely many solutions of the form $x = 7 - \frac { 3 } { 2 } z , y = 2 z , z = z$

Quizplus · Accepted Answer

The system of equations has two equations and three unknowns, which typically results in infinitely many solutions. By subtracting the second equation from the first, we eliminate $y$ and find a relationship between $x$ and $z$, leading to the form given in option A.

Find the Solution or Solutions, If Any Exist, to the System