Use Cramer's Rule, if possible, to solve the system of linear equations.
-$$\left\{ \begin{aligned}
2 x + 5 z & = 33 \
- 5 x + 6 y - 3 z & = 7 \
- 2 x - 4 y & = - 36
\end{aligned} \right.$$
A) $( 4,7,5 )$
B) $( 5,5,5 )$
C) $( 7,5,7 )$
D) $( 4 , - 7 , - 5 )$

Question

Quizplus · Accepted Answer

Cramer's Rule can be used to solve a system of linear equations when the system has the same number of equations as unknowns, and the determinant of the coefficient matrix is non-zero. This system has three equations and three unknowns (x, y, z), making it suitable for Cramer's Rule. Solving it using Cramer's Rule yields the solution $x = 4$, $y = 7$, and $z = 5$, which corresponds to choice A.

Use Cramer's Rule, If Possible, to Solve the System of Linear