Question 298024
3x+4y+z=7
   2y+z=3
-5x+3y+8z=-31

the first step to solving this problem is to eliminate x form the 1st and last eqaution so you can solve for y or z

3x+4y+z=7
-5x+3y+8z=-31

to eliminate x you need to multiply the first equation by 5 and the second equation by 3 and you get

15x+20y+5z=35
-15x+9y+24z=-93

and the x's cancle out and you are left with

20y+5z=35
9y+24z=-93

then you add the like terms in both of the ewuations and you should get

29y+29z=-58

once you have this equation you can use it with the 2nd equation from the origional equations 

29y+29z=-58
2y+z=3

then you need to choose a variable to solve for
solve for y and to do so you need to sliminate z and multiply the second equation by -29

29y+29z=-58
-58y-29z=-87

then you add the two equations together and z canles out

-29y=-148

devide both sides by -29

y=5

now that you know y you can plug it into one of above equations

3x+4y-7=7

3x+4(5)-7=7
3x+20-7=7
3x+13=7
3x=-6
x=-2

now that you know both x and y you can plug them both into one of origional equations

2y+z=3

2(5)+z=3
10+z=3
z=-7

so the final answer is (-2,5,-7)