Solve the following system of equations.

Question

2x - y + z = -3

2x + 2y + 3z = 2

3x - 3y - z = -4?

Answer 1

Elimination method :

The system of equations are

2x - y + z = - 3     →(1)

2x + 2y + 3z = 2   →(2)

3x - 3y - z = - 4    →(3)

Write the equations (1) & (2) in column form, then subtact them, to eliminate the x - variable.

2x - y + z = - 3

2x + 2y + 3z = 2

(-)____________________

- 3y - 2z = - 5 ⇒ 3y + 2z = 5 →(4)

Multiply eq(2) by 3 and eq(3) by 2, and then write the equations in column form, then subtract them, to eliminate the x - variable.

6x + 6y + 9z = 6

6x - 6y - 2z = - 8

(-)____________________

12y + 11z = 14  →(5)

Multiply eq(4) by 4 ,then write the equations in column form, then subtract them, to eliminate the y - variable.

12y + 8z = 20

12y + 11z = 14

(-)_______________

- 3z = 6 ⇒ z = - 6/3 = - 2.

Substitute the z - value in eq (4), and solve for y.

3y + 2(- 2) = 5

3y - 4 = 5

3y = 5 + 4 = 9

⇒ y = 9/3 = 3.

Substitute the values y = 3, z = - 2 in eq(1), and solve for x.

2x - 3 + (- 2) = - 3

2x - 3 - 2 = - 3

2x - 5 = - 3

2x = - 3 + 5 = 2

⇒ x = 2/2 = 1.

The solution of the system is x = 1, y = 3, and z = - 2.