Two integers have a sum of 2, and a difference of 12. find the two integers

Explanation:

Let x and y be the two integers where x > y.

The two integers have a sum of x+y and this is equal to 2, so x+y = 2. Solve for y to get y = -x+2

The two integers also have a difference of 12, so x-y = 12. Plug in y = -x+2 and solve for x

x-y = 12

x - ( y ) = 12

x - ( -x+2 )  = 12 ... replace y with -x+2

x + x - 2 = 12

2x - 2 = 12

2x - 2+2 = 12+2 adding 2 to both sides

2x = 14

2x/2 = 14/2 divide both sides by 2

x = 7

Use this x value to find y

y = -x+2

y = -7+2

y = -5

As a check,

x+y = 7+(-5) = 7-5 = 2 ... we get a sum of 2

x-y = 7-(-5) = 7+5 = 12 ... and get a difference of 12

the answers have been confirmed

ratio is 2 : 9

the answer is three

13.5 : 3