The sum of two numbers, x and y, is 12. The difference of x and two times y is 6. What are the values of x and y?

Question

anonymous · Answer

@whpalmer4

whpalmer4 · Answer

Write the equations:
The sum of two numbers, x and y, is 12:
$$x+y = 12$$The difference of x and two times y is 6:$$x-2y=6$$

Now you have a system of two equations in two unknowns. Do you know how to solve it?

anonymous · Answer

I do not sir

whpalmer4 · Answer

Okay, there are a number of ways to do so, but two of the easiest are substitution and elimination.  Let's do substitution.  Can you solve the first equation $(x+y=12$) for either $x$ or $y$?  Your choice.

whpalmer4 · Answer

Okay, we'll solve for $x$.  $$x+y=12$$Subtract $y$ from both sides$$x+y-y=12-y$$$$x=12-y$$Was that so difficult?

Now, in the second equation, $x-2y=6$, you need to replace $x$ with $(12-y)$wherever you see it.  That will give you an equation in terms of $y$ only.  Solve that, and you'll have your value of $y$.  Then use it in $x = 12-y$ to find $x$.

anonymous · Answer

x=12-y ?

anonymous · Answer

10?

whpalmer4 · Answer

10?  What is 10?  The number of pizzas you're going to order for me?

jdoe0001 · Answer

better be small-size pizzas, I could only eat one family-size myself =), couldn't eat 2 though

whpalmer4 · Answer

So, what are the answers to this problem?

whpalmer4 · Answer

@jdoe0001 I'll shoot you a PM when the pizzas arrive, you can come help me eat them :-)