Help me with solving problems using two variables and systems of two equation please

Okay. So here is the problem:

One number is 4 less than another number. The sum of the two numbers is four times their difference. What are the two numbers?

Please help me solve the problem using two variables and the system of two equations please and thank you. Also, please explain well how you got the answer. THANKS.

Let's say the numbers are A and B:

1) A = B -4

2) (A + B) = 4 • (B -A)

To solve the problem, use equation 1 and substitute it into equation 2

B-4 + B = 4 B - 4B --16


2B -4 = 4 B -4B +16

2 B = 20

B = 10

Substituting this into the first equation:

A= 10 -4
A=6

Just translate the description directly into symbols.
"One number", you do not know but it is described using "another number". "Another number", call it variable y.

One number is 4 less than another number:
y-4 is the "one number".

Sum of the two numbers:
(y-4)+y

Is four times their difference:
=4|((y-4)-y)|

Put it all together:
(y-4)+y=4(y-(y-4))
Solve for y.

Let the first number be x and the second number be y
So, the two equations are: x= y-4 and x+y=4(x-y)

By substitution, y-4+y=4(y-4-y)
2y-4=4(-4)
2y-4= -16
2y= -12
y= -6

x= -6-4
x= -10

x-4=y
x+y=4(y-x)

plug in (x-4) for your value of y in the second equation

x+(x+4)=4((x-x+4))
2x+4=4(4)
2x+4=16
2x=12
x=6
so when you plug your x into your very first equation you get y=10

hope that helps :)

Let x=smaller number
x+4= larger number
x+x+4=4(x+4-x)
2x+4=16
x=6, x+4=10