Please help with algebra 2?

Question

What is the value of y in the solution of the system of
equations?
2x + y + z = 13
2x - y - 3z = -3
x + 2y + 4z = 20

Answer 1

2x + y + z = 13    -(1)

2x - y - 3z = -3     -(2)

x + 2y + 4z = 20  -(3)

Subtract from first equation to seccond equation

2y + 4z = 16 -(4)

Substitute the 2y + 4z = 16 in the third equation x + 2y + 4z = 20

x + 16 = 20

Subtract 16 from each side

x + 16 - 16 = 20 - 16

x + 0 = 4

x = 4

Substitute x = 4 in the first equation 2x + y + z = 13

8 + y + z = 13

Subtract 8 from each side

y + z = 13 - 8

y + z = 5  

Multiply each side by 4

4(y + z) =4( 5)

4y + 4z = 20

2y + 2y + 4z = 20

Substitute 2y + 4z = 16 in the 2y + 2y + 4z = 20

There fore 2y + 16 = 20

Subtract 16 from each side

2y + 16 - 16 = 20 -16

2y + 0 = 20 - 16

2y = 4

Divide each side by 2

y = 2

The value of y in the solution of system of equations : 2 .