Solve the system analytically. \[ \begin{array}{r} x+y+z=-4 \\ 2 x+5 y+2 z=-26 \\ -x+8 y-3 z=-56 \end{array} \]

Step 1 ：First, add the first and the third equation to eliminate x: \( (x + y + z) + (-x + 8y - 3z) = -4 + -56 \), which simplifies to \( 9y - 2z = -60 \)

Step 2 ：Next, multiply the first equation by 2 and subtract the second equation from the result to eliminate x: \( 2*(x + y + z) - (2x + 5y + 2z) = 2*-4 - -26 \), which simplifies to \( -3y = -2 \)

Step 3 ：Solve the system of two equations \( 9y - 2z = -60 \) and \( -3y = -2 \) to find the values of y and z. From the second equation, we find that \( y = \frac{2}{3} \)

Step 4 ：Substitute \( y = \frac{2}{3} \) into the first equation to find z: \( 9*\frac{2}{3} - 2z = -60 \), which simplifies to \( z = 3 \)

Step 5 ：Finally, substitute \( y = \frac{2}{3} \) and \( z = 3 \) into any of the original equations to find the value of x. Using the first equation, we find that \( x = -1 \)

Step 6 ：The solution to the system of equations is \(\boxed{x = -1, y = -6, z = 3}\)