Solve the following system of equations; 2x + 2y + z = 10, 3x - y + 3z = 10, 2x + 3y - 2z = 6

Solution:

We have a system of linear equations of three variables.

Given:

2x + 2y + z = 10 --------->(1)

⇒ 3x - y + 3z = 10 --------->(2)

⇒ 2x + 3y - 2z = 6 --------->(3)

Let us solve them using the substitution method.

By solving equation [1] for the variable z, we get

Substitute z = 10 - 2x -2y in equation (2).

⇒ 3x − y + 3 (10 - 2x -2y ) = 10

⇒ 3x -y + 30 - 6x - 6y = 10

⇒ - 3x - 7y = - 20 --------->(4)

Substitute z = 10 - 2x -2y in equation (3).

⇒ 2x + 3y − 2 (10 - 2x -2y) = 6

⇒ 2x + 3y - 20 + 4x + 4y = 6

⇒ 6x + 7y = 26 ---------> (5)

Add equation (4) and (5).

⇒ (- 3x - 7y = - 20) + (6x + 7y = 26)

⇒ 3x = 6

⇒ x = 2

Put the value of x = 2 in equation (5).

⇒ 6x + 7y = 26

⇒ 6 (2) + 7y = 26

⇒ 7y = 26 - 12

⇒ y = 2

Put the value of x = 2 and y = 2 in z = 10 - 2x - 2y.

⇒ z = 10 - 2(2) - 2(2)

⇒ z = 10 - 4 - 4

⇒ z = 2

Thus x= 2, y =2 and z =2

---

Solve the following system of equations; 2x + 2y + z = 10, 3x - y + 3z = 10, 2x + 3y - 2z = 6

Summary:

By solving the system of linear equations 2x + 2y + z = 10, 3x - y + 3z = 10, 2x + 3y - 2z = 6; we get (x, y, z) = (2, 2, 2)