Solve the given system

Question

6x-y+4z=6

-x -3y+z=31

2x+2y-5z=-42

Answer 1

Eliminates x....

Eq1 + 6 * Eq2:

-19y + 10z = 192

Eq 3 + 2 * eq2:

-4y + -3z = 20

Changes the signs:

19y - 10z = -192

4y + 3z = -20

Solves by elimination:

3 ( 19y - 10z = -192)

10 ( 4y + 3z = -20)

57y - 30z = -576

40y + 30z = -200

97y = -776

y = -8

4(-8) + 3z = -20

-32 + 3z = -20

3z = 12

z = 4

original 2nd equation:

-x - 3(-8) + 4 = 31

-x + 24 + 4 = 31

-x + 28 = 31

-x = 3

x = -3

the solution set is {x=-3, y=-8, z = 4}