Question

Solve the following system of equations.
x + 4y + z = -10
3x - 3y + 6z = -21
x + 2y + 2z = -10

Answer

(1, -2, -3)
(-4, -1, -2)
(-3, -2, -3)
(2, -2, -4)

Answer 1

(-4,-1,-2)
let me know if you need to show work

Answer 2

Yep if you row reduce the augmented matrix [A b] you will get x = -4, y=-1 and z=-2 or the point (-4,-1,-2)
A is the coefficient matrix of the system of equations, b is the 1x3 matrix that you augment with the coefficient matrix to produce a 3x3 matrix [A b]

Answer 3

Another way of solving the equation above it to graph the equations and find the intersecting point.

Or use Cramer's rule to solve for the point (x,y,z)

Or better yet you could solve for x by observing that \[x = A^{-1}b\]
A^(-1) = 1/det(A)*adjugate(A)