SOLUTION: Solve for x, y, and z. Use only linear combination and/or substitution. Do not use matrices. 2x - 12y + 3z = -19 4x + 6y - 2z = 14 6x - 9y - 4z = 13

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve for x, y, and z. Use only linear combination and/or substitution. Do not use matrices. 2x - 12y + 3z = -19 4x + 6y - 2z = 14 6x - 9y - 4z = 13       Log On


   

Question 356680: Solve for x, y, and z. Use only linear combination and/or substitution. Do not use matrices.
2x - 12y + 3z = -19
4x + 6y - 2z = 14
6x - 9y - 4z = 13
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.2x+-+12y+%2B+3z+=+-19
2.4x+%2B+6y+-+2z+=+14
3.6x+-+9y+-+4z+=+13
From eq. 1,
2x=12y-3z-19
Multiply by (2),
4x=24y-6z-38
Multiply by (3),
6x=36y-9z-57
Now substitute into eq. 2 and eq. 3,
%2824y-6z-38%29%2B6y-2z=14
30y-8z=52
4.15y-4z=26
.
.
%2836y-9z-57%29-+9y+-+4z+=+13
5.27y-13z=70
From eq. 4,
4z=15y-26
z=%2815%2F4%29y-13%2F2
Substitute into eq. 5,
27y-13%28%2815%2F4%29z-13%2F2%29=70
108y-13%2815z-26%29=280
108y-195y%2B338=280
-87y%2B338=280
-87y=-58
y=58%2F87
highlight%28y=2%2F3%29
Then,
z=%2815%2F4%29%282%2F3%29-13%2F2
z=5%2F2-13%2F2
z=-8%2F2
highlight%28z=-4%29
Then,
2x=12%282%2F3%29-3%28-4%29-19
2x=8%2B12-19
2x=1
highlight%28x=1%2F2%29