Solve the following systems of 3-variable linear equations.

1.
2x + y = 1
3y + z = 1
x + 4z = 1

x = 9/25, y = 7/25, z = 4/25

Explanation:

step 1: solve for y in first equation to use substitution

y = -2x + 1

step 2: insert into second equation to eliminate y variable and work with two variables

3(-2x+1) + z = 1 (now distribute)

-6x + 3 + z = 1 (bring over the -3)

-6x + z = -2

step 3: now left with -6x + z = -2 and x + 4z = 1, so eliminate z

-6x + z = -2 (multiply by 4)

4(-6x + z = -2)

-24x + 4z = -8

-

x + 4z = 1 (brought down third equation)

-25x = -9

x = 9/25

then just plug in x into the third equation to solve for z, followed by plugging it into the first equation to solve for y. you should end with y = 7/25 and z = 4/25