SOLUTION: Please help me solve this equation: 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

Question 175693: Please help me solve this equation: 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?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"the sum of two numbers is 13" translates to

"Two times the first number minus three times the second number is 1" translates to

So we have the system of equations:

Let's solve this system by substitution.

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Add 39 to both sides

Combine like terms on the right side

Divide both sides by 5 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

This means that the first number is 8 and the second number is 5
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