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# Solve the following system of equation; 2x + 3y - z = 1, 3x + y + 2Z = 12, x + 2y - 3 = - 5

**Solution:**

Given is a system of linear equations of 3 variables.

2x + 3y - z = 1 --- (1)

⇒ 3x + y + 2z = 12 --- (2)

⇒ x + 2y - 3 = - 5

⇒ x + 2y = - 2 --- (3)

Let us use the substitution method for solving the system of linear equations simultaneously.

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

⇒ z = 2x + 3y - 1..............(4)

Substitute the value of z = 3x + 6y - 1 in equation [2]

⇒ 3x + y + 2× (2x + 3y - 1 ) = 12

⇒ x + y = 2 .............. (5)

By subtracting equation (5) from (3), we get

y = - 4

Substitute the value of y = - 4 in equation [5]

⇒ x + (- 4) = 2

⇒ x = 6

Substitute the values of x and y in equation (1), we get

⇒ 2 (6) + 3 (- 4) - z = 1

⇒ 12 - 12 - z = 1

⇒ 0 - z = 1

⇒ z = -1

## Solve the following system of equation; 2x + 3y - z = 1, 3x + y + 2Z = 12, x + 2y - 3 = - 5

**Summary:**

By solving the system of linear equations 2x + 3y - z = 1, 3x + y + 2Z = 12, x + 2y - 3 = - 5 ; we get (x, y, z) = (6, - 4, -1).

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