Question 868335
Let x and y be the two unknown numbers. Let's make x the larger number. So x > y.



"The sum of two numbers is 76" means that when you add them together, you get 76, so {{{x+y=76}}}



"their difference is 52" means that when you subtract them, you get 52, so {{{x-y=52}}}



The system of equations is



{{{system(x+y=76,x-y=52)}}}



We'll use this system to solve for x and y.



Start by adding the equations (add the left sides separately and the right sides separately)


<pre>
x  +  y = 76
x  -  y = 52
--------------
2x + 0y = 128
</pre>



So that means 2x = 128 and isolating x (divide both sides by 2) gives us x = 64



Now we use x = 64 to find y. So we pick on any equation that has both x & y in it, plug in x = 64 and solve for y. I'm going to pick the first equation.



x+y=76



64+y=76



y=76-64



y=12



=======================================================



So we've found that x = 64 and y = 12. 



Therefore, the two numbers are 64 and 12.



Notice how 64+12 = 76 and how 64-12 = 52. So the answers check out.