The sum of two numbers is 24. seven times the smaller number is the same as 5 times the larger number. find the number. (would anyone mind explaining it at a beginner's algebra 1 kind of explanation? )

X+y=24
and
7x=5y or 7x-5y=0

You have to solve this by a system of equations by elimination. You have to get the first equation to have a positive 5 in it with the "y" so it cancels, or eliminates the -5 in the second equation. To do this, you multiply every quantity by 5.

5(x+y=24)
5x+5y=120

This new equation is equal to "x+y=24". Now, you add this equation to "7x-5y=0". To get the value of x because the y's cancel each other out.

5x+5y=120
+7x-5y=0

12x=120
x=10

Now substitute in the x value (10) into any one of the equations. I picked "x+y=24".

10+y=24
y=14

So your two numbers are 10 and 14

The first answer is correct