SOLUTION: The sum of the two number is 3. The difference of twice the larger number and 3 times the smaller number is 16. Find the numbers.

Question 185984: The sum of the two number is 3. The difference of twice the larger number and 3 times the smaller number is 16. Find the numbers.
Answer by joecbaseball(37) (Show Source): You can put this solution on YOUR website!
You must first set up a series of equations:
The sum of the two number is 3.
We write x + y = 3.
The difference of twice the larger number and 3 times the smaller number is 16.
Assume x is larger. (It doesn't make any difference, however.)
2x - 3y = 16.
So your system has two equations:
x + y = 3
2x - 3y = 16
There are a number of ways to solve a system of equations like this. I will use the "substitution method" where I will solve for x in the first equation and substitute it in for the x term in the second equation.
x + y = 3 ======> x = 3 - y
Substituting that value in for x in the second equation gives:
2(3 - y) - 3y = 16
Simplifying gives you:
6 - 2y - 3y = 16
Simplifying that gives you:
6 - 5y = 16
Solving for y gives you:
5y = -10, so, y = -2
Now substitute y = -2 back into our first equation:
x + (-2) = 3, and solve for x:
x = 5.
You can check these answers by plugging them back into both equations to see if they work. You will find that they do.
Good luck
JoeC
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