solve this system using either elimination or substitution:

Question

2x+y-z=5
3x-y+2z=-1
x-y-z=19

Answer 1

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 y - variable.

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 : .

The two equations 2 and 3 contains same coefficient of y - variable.

Write the equations 2 and 3 in column form and subtract the corresponding columns to eliminate y - 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 z - variables are 1 and 3 and their least common multiple is 3, so multiply each equation by the value  that will make the z - coefficient 3.

To get two equations 4 and 5 that contain opposite terms multiply the fourth equation by negative 3.

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

.

The resultant equation is .

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

The fourth equation: .

.

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

The third equation: .

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The solution .