Answer
$\{(1,-1,4)\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
4x-3y+2z=15\\
-2x+y-3z=-15\\
5x-5y+2z=18
\end{cases}$
Compute $D,D_x,D_y,D_z$:
$D=\begin{vmatrix}4&-3&2\\-2&1&-3\\5&-5&2\end{vmatrix}=4(-13)-(-3)(11)+2(5)=-9$
$D_x=\begin{vmatrix}15&-3&2\\-15&1&-3\\18&-5&2\end{vmatrix}=15(-13)-(-3)(24)+2(57)=-9$
$D_y=\begin{vmatrix}4&15&2\\-2&-15&-3\\5&18&2\end{vmatrix}=4(24)-15(11)+2(39)=9$
$D_z=\begin{vmatrix}4&-3&15\\-2&1&-15\\5&-5&18\end{vmatrix}=4(-57)-(-3)(39)+15(5)=-36$
Determine $x$:
$x=\dfrac{D_x}{D}=\dfrac{-9}{-9}=1$
Determine $y$:
$y=\dfrac{D_y}{D}=\dfrac{9}{-9}=-1$
Determine $z$:
$z=\dfrac{D_z}{D}=\dfrac{-36}{-9}=4$
The solution set is:
$\{(1,-1,4)\}$
