Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { r }
x + y + z = 9 \
2 x - 3 y + 4 z = 7
\end{array}$$
A) Cramer's rule does not apply since $D = 0 ; \left\{ \left\{ \frac { z + 34 } { 5 } , \frac { 2 z + 11 } { 5 } , z \right) \right\}$
B) Cramer's rule does not apply since $\mathrm { D } = 0 ; \left\{ \left[ \frac { - 7 \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } - 11 } { 5 } , \mathrm { z } \right) \right\}$
C) Cramer's rule does not apply since $D = 0 ; \varnothing$
D) Cramer's rule does not apply since $D = 0 ; \left\{ \left( \frac { - 7 z + 34 } { 5 } , \frac { 2 z + 11 } { 5 } , z \right) \right\}$

Question

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { r } 
x + y + z = 9 \
2 x - 3 y + 4 z = 7
\end{array}$$
A) Cramer's rule does not apply since $D = 0 ; \left\{ \left\{ \frac { z + 34 } { 5 } , \frac { 2 z + 11 } { 5 } , z \right) \right\}$
B) Cramer's rule does not apply since $\mathrm { D } = 0 ; \left\{ \left[ \frac { - 7 \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } - 11 } { 5 } , \mathrm { z } \right) \right\}$
C) Cramer's rule does not apply since $D = 0 ; \varnothing$
D) Cramer's rule does not apply since $D = 0 ; \left\{ \left( \frac { - 7 z + 34 } { 5 } , \frac { 2 z + 11 } { 5 } , z \right) \right\}$

Quizplus · Accepted Answer

Cramer's rule requires a square system of equations (same number of equations as unknowns), and here we only have 2 equations for 3 unknowns, making $D = 0$ and Cramer's rule inapplicable. The correct solution set is given by the parametric form in option D, indicating a family of solutions depending on the value of $z$.

Use Cramer's Rule to Solve the System of Equations x+y+z=92x−3y+4z=7\begin{array} { r } x + y + z = 9 \\2 x - 3 y + 4 z = 7\end{array}x+y+z=92x−3y+4z=7​

Use Cramer's Rule to Solve the System of Equations $\begin{array} { r } x + y + z = 9 \\2 x - 3 y + 4 z = 7\end{array}$