The sum of two numbers is 13. Two times the first number minus three times the second number is 1. If you let x stand for the first number and y for the second number, what are the two numbers?

A. x = 5, y = 8
B. x = –5, y = –8
C. x = –8, y = –5
D. x = 8, y = 5

Question

The sum of two numbers is 13. Two times the first number minus three times the second number is 1. If you let x stand for the first number and y for the second number, what are the two numbers? 
    
A. x = 5, y = 8
B. x = –5, y = –8
C. x = –8, y = –5
D. x = 8, y = 5

zzr0ck3r · Answer

x+y=13
2x-3y=1

Solve the first one for y and plug that into the second one and solve that for x.

mathstudent55 · Answer

Since you are given choices, you can "cheat" and try each set of numbers from the choices and see which one makes the statements true.

jakyfraze · Answer

is it A?

mathstudent55 · Answer

First, do both numbers of each choice add to 13?
If they don't eliminate that choice.

Then to check the second statement, multiply the first number by 2 and the second number by 3, and subtract the second product from the first one.
If the difference is not 1, it is not the answer.

zzr0ck3r · Answer

I would really recommend not trying this method. You should learn to solve the system of equations as that is obviously the point of this exercise.  If you are taking a written test ever in this class, I guarantee they will not be giving you the choices.

zzr0ck3r · Answer

$x+y=13 \implies y=13-x$

Now that we have the first equation in terms of $y$ we can plug it into the second equation where we see a $y$

$2x-3y=1 $ becomes $2x-3(13-x)=1$. Note I just changed $y$ to $13-x$ because the first equation says $y=13-x$.

Now you can solve for $x$.

After you get the answer for $x$, plug that into $y=13-x$ to find the answer for $y$.

mathstudent55 · Answer

I agree with @zzr0ck3r 
The "cheating" method I wrote about above is best left for just checking your answer once you find the solution by writing and solving a system of equations.

zzr0ck3r · Answer

It is odd to tell a student the hard way is better lol. Logically there is no reason that the "cheating" method is best, but we have to make assumption about the class as education has gotten this bad. 

Sometimes explaining the logic on why we should not take the "cheat routes" is harder than the logic needed to do the original problem...

zzr0ck3r · Answer

I teach this class, and I often find myself lying to the class, e.g. domain of functions questions make no sense. But if we tell them the truth, it is way to big and they get lost.

jakyfraze · Answer

zzr0ck3r@ i really understand what your saying :(

jakyfraze · Answer

X=8 y=5

zzr0ck3r · Answer

you do or don't understand what I am saying? You said 'do' but put a frowny face.

jakyfraze · Answer

zzr0ck3r@ yes i do i didn't mean to put a frown face