Elimination method :

The system of equations are $\"\"$ .

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

The two equations 1 and 2 contains opposite coefficient of z - variable.

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

$\"\"$

The resultant equation is taken as fourth equation : $\"\"$ .

To get two equations 2 and 3 that contain opposite terms multiply the second equation by 5 and multiply the third equation by 3.

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

$\"\"$

The resultant equation is taken as fifth equation : $\"\"$ .

Solve the system of two equations with two variables.

Neither variable has a common coefficient in equation 4 and 5.The coefficient of the y - variables are -1 and 17 and their least common multiple is -17, so multiply each equation by the value that will make the y - coefficient -17.

To get two equations 4 and 5 that contain opposite terms multiply the fourth equation by 17.

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

$\"\"$

The resultant equation is : $\"\"$ .

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

The fourth equation : $\"\"$ .

$\"\"$

$\"\"$ .

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

The third equation: $\"\"$ .

$\"\"$

$\"\"$ .

The solution is x = 0, y= 2,and z = 0.