trinabrowning37 said:

the sum of two numbers is 22. Five times one number is equal to 6 times the second number. Find the numbers; Now I know the numbers are 10 and 12 becuz of figuring it out in my head, but my question is how would this be set up and figured out using the algebra method

thanks in advance

Always start by naming things. In this case you are looking for two numbers. Name them something and write it down...

Here's one approach using two equations in two unknowns.

Let x represent one of the numbers.

Let y represent the other number.

"the sum of two numbers is 22" becomes x + y = 22

"Five times one number is equal to 6 times the second number." becomes 5x = 6y.

Now, solve simultaneously.