# How to Solve 3 Variable Linear Equations

This worksheet may help you how to solve the 3 variable linear equations.
Example
Solve the following equations and find the value of x, y & z.
1x - 1y + 2z = 5 --------------- (1)
2x + 1y - 1z = 1 --------------- (2)
3x - 2y + 3z = 8 --------------- (3)

(1)==========> 1x - 1y + 2z = 5
(2)==========> 2x + 1y - 1z = 1
Add(1)+(2)====>3x + 0 + 1z = 6 --------- (4)

Multiply Equation (2) by 2 and add with equation (3)
(2)x2==========> 4x + 2y - 2z = 2
(3)============> 3x - 2y + 3z = 8
Add(2)x2+(3)====>7x + 0 + 1z = 10 ---------- (5)

Subtract Equation (3) with 2 x Equation (1)
(3)=============> 3x - 2y + 3z = 8
2x(1)===========> 2x - 2y + 4z = 10
Sub(3)-2x(1)==>1x + 0 - 1z = -2 ----------- (6)

From Equation (4) & (5) we get,
(4)========> 3x + 0 + 1z = 6
(5)========> 7x + 0 + 1z = 10
Sub(4)-(5)===> -4x = -4

Hence x = 1
Substitute the value of X in the equation 6 we get,
x - z = -2
1 - z = -2
z = 3
Substitute the value of x = 1 & z = 3 in the equation 1 we get,
1x - 1y + 2z = 5
1 - y + 2(3) = 5
-y = 5 - 7
- y = - 2
y = 2

Hence the value of x, y & z is,
x = 1
y = 2
z = 3

The above worksheet is to help you understand how to solve the 3 variable linear equations, when try such calculations on your own this 3 equation 3 unknown solver can be used to verify your results.