Question

Solve the equations with 3 linear variables 
6x-4y+5z=31
5x+2y+2z=13
x+y+z=2

Answer 1

The system of equations are 6x  - 4y + 5 z = 31 -------------> (1)

                                           5x + 2y + 2z = 13 -------------> (2)

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

Multiply equation (2) by 2, then write the equations (1) & (2) in column form, and then add them.

6x - 4y + 5z = 31

10x + 4y + 4z = 26

( + )______________

16x + 9z = 57 -------> (4)

Multiply equation (3) by 2, write the equations (2) & (3) in column form, and then Subtract them each other.

5x + 2y + 2z = 13

2x + 2y + 2z = 4

( - )______________

3x = 9

x = 9/3 = 3.

Substitute x = 3 in equation (4).

16x + 9z = 57

16(- 1) + 9z = 57

- 16 + 9z = 57

9z = 57 + 16 = 73

z = 73/9.

Substitute the values x = 3 and z = 73/9 in equation (3).

(3) + y + (73/9) = 2

y = 2 - 3 - 73/9

y = - 1 - 73/9

y = (- 9 - 73)/9 = - 82/9.

The solution is x = 3, y = - 82/9 and z = 73/9.