QuestionUse Cramer's rule to solve the system of equations. $$\begin{array}{c} 5 x+2 y-4 z=-10 \\ -4 x+8 y-3 z=47 \\ 4 x+5 y-3 z=13 \end{array}$$ a. $(3,6,-2)$ c. $(-2,6,3)$ b. $(-2,3,6)$ d. $(6,-2,3)$

Studdy Solution
Verify the solution by substituting back into the original equations:
Substitute $x = -2$, $y = 6$, $z = 3$ into each equation:
1. $5(-2) + 2(6) - 4(3) = -10$ $ -10 + 12 - 12 = -10 \quad \text{True} \]
2. $-4(-2) + 8(6) - 3(3) = 47$ $ 8 + 48 - 9 = 47 \quad \text{True} \]
3. $4(-2) + 5(6) - 3(3) = 13$ $ -8 + 30 - 9 = 13 \quad \text{True} \]
The solution is verified.
The correct solution is $(-2, 6, 3)$, which corresponds to option c.