Question

solving systems of linear equations in three variables-
ok i dont know how to do this! I need help! heres the problem:

2x+y+z=-10
-x-4y+z=12
2x+2y+3z=13

thank you so much!

Answer 1

well you have 3 equations in 3 unknowns, and you want to reduce to to 2 equations in 2 unknowns

label the equations top = 1 middle = 2 and bottom =3

the easiest elimination is x so

equation 2 times 2 + equation 1

2x + y + z = -10
-2x - 8y + 2z = 24
-----------------
-7y + 3z = 14 this is equation 4

then equation 2 times 2 + equation 3

-2x -8x + 2z = 24
2x + 2y + 3z = 13
----------------
-6y + 5z = 37 equation 5

now you have 2 equations in 2 unknowns.... so eliminate z.

equation 4 times 5 + equation 5 times - 3

-35y + 15z = 70
18y -15z = -111
---------------
-17y = -41

so you can now solve for y.

then when you get it subsitute into either equation 4 or 5 to find z

when go to equation 1 and substiute y and z to find x.

I can tell you the solution contains ugly fractions.

hope it helps