The sum of two numbers is 35. their difference is 65. find the numbers.

The numbers are 50 and -15.

Step by step:

Let X + Y = 35 (i)
and X - Y = 65 (ii)
Find X, Y = ... ?

From (i),
X + Y = 35
substract Y from both sides,
X + Y - Y = 35 - Y
X = 35 - Y (iii)

substitute (iii) into (ii),
X - Y = 65
(35 - Y) - Y = 65
35 - 2Y = 65
substract 35 from both sides,
35 - 35 - 2Y = 65 - 35
-2Y = 30
divide -2 from both sides,
-2Y/-2 = 30/-2
Y = -15

substitute Y=-15 into (iii),
X = 35 - Y = 35 - (-15) = 35 + 15 = 50

So, X = 50 and Y = -15.