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

answer: the net deposit amount   (option c)

in order to fill in the deposit slip, michael needs to fill in the amount that he wants to deposit in the bank. without the net deposit amount, he will not be able to deposit the money because it is mandatory for him to mention it, as the bank needs to maintain a record to avoid any inconveniences for the bank and michael in the future.

the bank officer checks and verifies the amount received against the amount written on the deposit slip to process the slip.