Two numbers that have a sum of 100 and a diffrence of 6

x and y are the two numbers, which are unknown for now. Their sum is 100, so x+y = 100. Their difference is 6, so x-y = 6 (assume x is the larger value)

The system of equations we have is

x+y = 100

x-y = 6

Add the equations straight down. The x terms combine to x+x = 2x. The y terms cancel out because y+(-y) = y-y = 0y = 0. The right hand sides combine to 100+6 = 106

So we end up with 2x = 106. Divide both sides by 2 to get x = 53.

If x = 53, then...

x+y = 100

53+y = 100

y = 100-53

y = 47

Check:

53 + 47 = 100

53 - 47 = 6

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