Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the numbers.
+2441 Number 1:5
Number 2:8
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.
\(2x+y=18\)
\(4x-y=12\)
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:
\(6x=30\)
Divide by 6 on both sides:
\(x=5\)
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:
\(2(5)+y=18\)
Simplify 2*5:
\(10+y=18\)
Subtract 10 on both sides to isolate y, our second number:
\(y=8\)
