SOLUTION: solve the system of equations 3x+4y+z=7 2y+z=3 -5x+3y+8z=-31

Question 298024: solve the system of equations
3x+4y+z=7
2y+z=3
-5x+3y+8z=-31

Answer by alex224(8) (Show Source): You can put this solution on YOUR website!
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)

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