Use Cramer's rule to find the solution of the system, if possible. $$\left\{ \begin{array} { c }
x - y - z = 1 \
x + y + z = 19 \
- x - y + z = - 11
\end{array} \right.$$
A) $x = 10 , y = 5 , z = 4$
B) $x = 5 , y = 10 , z = 4$
C) $x = 4 , y = 5 , z = 10$
D) The system is inconsistent.
E) The equations are dependent.

Question

Use Cramer's rule to find the solution of the system, if possible. $$\left\{ \begin{array} { c } 
x - y - z = 1 \
x + y + z = 19 \
- x - y + z = - 11
\end{array} \right.$$
A) $x = 10 , y = 5 , z = 4$
B) $x = 5 , y = 10 , z = 4$
C) $x = 4 , y = 5 , z = 10$
D) The system is inconsistent.
E) The equations are dependent.

Quizplus · Accepted Answer

Cramer's rule involves calculating determinants to solve a system of linear equations. For this system, the determinant of the coefficient matrix is non-zero, allowing for the use of Cramer's rule. By applying Cramer's rule, we find that $x = 10$, $y = 5$, and $z = 4$, which matches option A.

Use Cramer's Rule to Find the Solution of the System {x−y−z=1x+y+z=19−x−y+z=−11\left\{ \begin{array} { c } x - y - z = 1 \\x + y + z = 19 \\- x - y + z = - 11\end{array} \right.⎩⎨⎧​x−y−z=1x+y+z=19−x−y+z=−11​

Use Cramer's Rule to Find the Solution of the System $\left\{ \begin{array} { c } x - y - z = 1 \\x + y + z = 19 \\- x - y + z = - 11\end{array} \right.$