9514 1404 393
Answer:
(x, y, z) = (2, 1, -5)
Explanation:
There are numerous equation solvers available on the web. The attached result is from one of them.
__
You may find it easier to solve these by hand if you eliminate fractions.
- 2x -y +z = -2
- x +3y -z = 10
- x +0y +2z = -8
The first step is to look to see what you have, then formulate a strategy for getting a solution. Because the equations containing y have opposite coefficients, one of which is -1, we choose to use those to eliminate y. Immediately, we will have two equations in x and z.
If you multiply the first equation by 3 and add that to the second, then you will eliminate y. The third equation already has y eliminated, so you will then have two equations in x and z.
3(2x -y +z) +(x +3y -z) = 3(-2) +(10)
6x -3y +3z +x +3y -z = -6 +10
7x +2z = 4 . . . . [eq4]
Subtracting the third equation from this eliminates z, so you have ...
(7x +2z) -(x +2z) = (4) -(-8)
6x = 12
x = 2
Substituting into the third equation gives ...
2 +2z = -8
2z = -10
z = -5
Then using the first equation, you have ...
y = 2x +z +2 = 2(2) +(-5) +2 = 1
(x, y, z) = (2, 1, -5)