Question

How to solve Linear Equation in three variables????​

Answer 1

4x - 3y + z = - 10 (i)

2x + y + 3z = 0 (ii)

- x + 2y - 5z = 17 (iii)

Pick two pairs:

4x - 3y + z = - 10

2x + y + 3z = 0

Eliminate the same variable from each system:

4x - 3y + z = - 10

2x + y + 3z = 0

4x - 3y + z = - 10

-4x - 2y - 6z = 0

-5y - 5z = - 10

2x + y + 3z = 0

- x + 2y - 5z = 17

2x + y + 3z = 0

-2x + 4y - 10z = 34

5y - 7z = 34

Solve the system of the two new equations:

-5y - 5z = - 10

5y - 7z = 34

-12z = 24

Thus,

z = - 2

substitute the value,

-5y - 5(- 2) = - 10

-5y = - 20

Thus,

y = 4

Substitute into one of the original equations:

- x + 2y - 5z = 17

- x + 2(4) - 5(- 2) = 17

- x + 18 = 17

- x = - 1

x = 1