The sum of two numbers is 100 and their difference is 80, what are the two numbers

x=90
y=10

Explanation:
Let x be equal to the first number.
Let y be equal to the second number.

We know that the sum of the two numbers is 100, so we can say that x+y=100.

We also know that the difference of the two numbers is 80, so we can also say that x-y=80

And now we have our two equations:

x+y=100
x-y=80

To find x and y, we first solve for one of the variables and plug it into one of the two equations to solve for the other. In this case, the easiest way to approach this question is to add both of the equations to cancel y out and solve for x (please check the picture attached for a better representation).

x+y=100
x-y=80
-> 2x=180

2x=180
Divide both sides by 2
2x/2=180/2
x=90

Now that we have found the value of the first number, x, we can plug it in to either of our two original equations to solve for y.

x+y=100
90+y=100
Subtract both sides by 90
90+y-90=100-90
y=10

Therefore, the value of x is 90 and the value of y is 10. Their sum is 100 and their difference is 80.

I hope this helps!