Answer: The two integers are 7 and -5
==============================================================
Step-by-step 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