Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the numbers.
In this problem, "one number" and "another number" are simply referring to variables like x and y. "Is" means equal to. Therefore, twice one number is simply 2 multiplied by a variable. For my variables, I'll simply use x and y.
This is a system of equations. Normally, I gravitate toward substitution, but I'll actually use elimination to solve this. Notice how there is a y-term and a negative y-term. I can add the equations together to get this:
Divide by 6 on both sides:
Okay, our first number is equal to five. To find the next number, y, substitute 5 into one of the equations. It doesn't matter which one; you'll get the same answer:
Subtract 10 on both sides to isolate y, our second number: