One number is 4 more than another. The difference between their squares is 80. What are their numbers?

Answer 1

Use x and x+4 as the numbers. So (x+4)² -x² =80 or x² +8x +16 -x² =80 which leaves 8x+ 16 = 80 and

8x=64 giving x= 8 and x+4 =12 so the numbers are 8 and 12.

Answer 2

One number, let's say A, is 4 more than another, let's say B.

If A is 4 greater than B, then B+4=A.

The difference between their squares (A², B²) is 80 so A²-B²=80

Your system of equations is:

B+4=A

A²-B²=80

Because A is already isolated you can substitute it into the second (ie. more complicated) equation

(B+4)²-B²=80

Expand

B²+8B+16-B²=80

Simplify and solve for B

8B+16=80

8B=64

B = 8

Put into first equation: A=B+4

A = 8+4 = 12

A=12 B=4.