QuestionQuestion 1, 11.1.45
Solve the given system of equations. If the system has no solution, say that it is inconsistent. $$\left\{\begin{array}{rr} x-2 y+3 z= & 7 \\ 2 x+y+z= & -1 \\ -3 x+2 y-2 z= & -3 \end{array}\right.$$

Studdy Solution
Check the solution $(x, y, z) = (-1, -1, 2)$ by substituting back into the original equations:
1. $x - 2y + 3z = 7$
$-1 - 2(-1) + 3(2) = 7$
$-1 + 2 + 6 = 7$
$7 = 7$ (True)
2. $2x + y + z = -1$
$2(-1) + (-1) + 2 = -1$
$-2 - 1 + 2 = -1$
$-1 = -1$ (True)
3. $-3x + 2y - 2z = -3$
$-3(-1) + 2(-1) - 2(2) = -3$
$3 - 2 - 4 = -3$
$-3 = -3$ (True)
All equations are satisfied.
The solution to the system of equations is:
$$(x, y, z) = (-1, -1, 2)$$