One number is 2 more than 3 times another. their sum is 22. find the numbers.

Make a system of equations.




Re-arrange the 2nd equation:



Subtract y to both sides:



Plug in -y + 22 for 'x' in the first equation.





Subtract 3y to both sides:



Subtract 22 to both sides:



Divide -4 to both sides:



Plug this into any of the two equations to find 'x':





Subtract 5 to both sides:



So one of the numbers is 5 and one of them is 17.