The system of equations are .

Use the elimination method to make a system of two equations in two variables.

To get two equations 1 and 2 that contain opposite coefficient of y - variable multiply the first equation by negative 4.

Write the equations 1 and 2 in column form and add the corresponding columns to eliminate y - variable.

The resultant equation is taken as fourth equation : 22x + 19z = - 252.

To get two equations 2 and 3 that contain opposite coefficient of y - variable multiply the second equation by 3 and multiply the third equation by 4.

Write the equations 2 and 3 in column form and add the corresponding columns to eliminate y - variable.

The resultant equation is taken as fifth equation : 30x + z = - 244.

Solve the system of two equations with two variables.

To get two equations 4 and 5 that contain opposite coefficient of z - variable multiply the fifth equation by negative 19.

Write the equations 4 and 5 in column form and add the corresponding columns to eliminate z - variable.

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The resultant equation is - 548x = 4384 ----> x = - 8.

Use one of the equation with two variables (Equation: 4 or 5) to solve for z.

The fifth equation: 30x + z = - 244.

30(- 8) + z = - 244

- 240 + z = - 244

z = - 4.

Solve for y using one of the original equations with three variables.

The first equation: - 5x + y - 4z = 60.

- 5(- 8) + y - 4(- 4) = 60

40 + y + 16 = 60

y + 56 = 60

y = 4.

The solution (x, y, z) = (- 8, 4, - 4).