The sum of two numbers is 580. the difference is 150. find the largest of the two numbers

X=small number
y=large number

x+y=580
y-x=150

y=580-x
(580-x)-x=150
-580          -580
-x-x=-430
-2x=-430
-2x/-2=-430/-2
x=215

215+y=580
-215     -215
y=365

FINAL ANSWER: The largest number is 365 and the small number is 215.

So,

We can "translate" these statements into mathematical open phrases.

"The sum of two numbers is 580."
x + y = 580

"The difference is 150."
x - y = 150

So we have our two equations:
x + y = 580
x - y = 150

It is easy to see that we can use Elimination by Addition by adding the two equations together and solving for x.

2x = 730

Divide both sides by 2.
x = 365

Substitute 365 for x in the first equation.
365 + y = 580

Subtract 365 from both sides.
y = 215

Check.
365 + 215 = 580
580 = 580

365 - 215 = 150
150 = 150

So the larger number is 365 and the smaller number is 215.  We are interested in the larger number, so the answer is 365.