Solve.
-4x + 4y + z = 15 2x - 5y - z = 17
2x + y + 3z = 17
A)No solution
B)(5, -2, 3)
C)(3, -2, 5)
D)(5, 3, -2)

Question

Quizplus · Accepted Answer

Rearranging the equations in matrix form, we have:
\begin{bmatrix} 4 & 4 & 1 \ 2 & -5 & -1 \ 2 & 1 & 3 \end{bmatrix} \begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 15 \ 17 \ 17 \end{bmatrix}
The determinant of the coefficient matrix is -63. Therefore, the system has a unique solution given by: 
\begin{align*} x &= \frac{1}{-63} \begin{vmatrix} 15 & 4 & 1 \ 17 & -5 & -1 \ 17 & 1 & 3 \end{vmatrix} = 5 \ y &= \frac{1}{-63} \begin{vmatrix} 4 & 15 & 1 \ -5 & 17 & -1 \ 1 & 17 & 3 \end{vmatrix} = -2 \ z &= \frac{1}{-63} \begin{vmatrix} 4 & 4 & 15 \ -5 & -5 & 17 \ 1 & 1 & 17 \end{vmatrix} = 3 \end{align*}
Therefore, the solution is (x,y,z) = (5,-2,3).

Solve. -4x + 4y + Z = 15 2x - 5y