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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
"the sum of two numbers is 13" translates to x%2By=13

"Two times the first number minus three times the second number is 1" translates to 2x-3y=1






So we have the system of equations:

system%28x%2By=13%2C2x-3y=1%29


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

x%2By=13 Start with the first equation


y=13-x Subtract x from both sides


y=-x%2B13 Rearrange the equation


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

Since y=-x%2B13, we can now replace each y in the second equation with -x%2B13 to solve for x



2x-3highlight%28%28-x%2B13%29%29=1 Plug in y=-x%2B13 into the second equation. In other words, replace each y with -x%2B13. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2x%2B%28-3%29%28-1%29x%2B%28-3%29%2813%29=1 Distribute -3 to -x%2B13


2x%2B3x-39=1 Multiply


5x-39=1 Combine like terms on the left side


5x=1%2B39Add 39 to both sides


5x=40 Combine like terms on the right side


x=%2840%29%2F%285%29 Divide both sides by 5 to isolate x



x=8 Divide



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


So the first part of our answer is: x=8



Since we know that x=8 we can plug it into the equation y=-x%2B13 (remember we previously solved for y in the first equation).



y=-x%2B13 Start with the equation where y was previously isolated.


y=-%288%29%2B13 Plug in x=8


y=-8%2B13 Multiply


y=5 Combine like terms



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


So the second part of our answer is: y=5




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

So our answers are:

x=8 and y=5


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