two numbers sum to 65. twice the first minus the second is 5. what are the numbers

Question

how can i find the numbers

Answer 1

Kevin -

 

Eric has the start to it right, but I'm going to take it one step further for you. 

When you have two equations and two variables, you can isolate one of the variables (rearrange the equation into x= or y= form) and insert that into the other equation. Here's what we're starting with. 

 

x + y = 65

2x - y = 5

 

I think the easiest way to do this is to rearrange the first equation into terms of y (y= form). We can do this simply by subtracting x from each side. 

 

x + y = 65

x + y - x = 65 - x

x + y - x = 65-x

y = 65 - x

 

Great! Now we can insert this "definition" of y into the OTHER equation, and then we'll have enough information to solve. 

 

2x - y = 5

2x - (65 - x) = 5

2x - 65 + x = 5

3x - 65 = 5

3x - 65 + 65 = 5 + 65

3x -65 + 65 = 70

3x = 70

x = 70/3

x = 23 1/3

 

Now we can insert our definition of x to replace the only x variable in our definition of y!

 

y = 65 - x

y = 65 - 23 1/3

y = 41 2/3

 

Now there you go! We got it! I hope you found this helpful!

Amanda

Answer 2

Adding Eric's equations you can eliminate y:

 

x+y = 65 ==> y = 65 - x
2x-y = 5

–––––––

3x+0=70

 

x = 70/3

 

y = 65 - 70/3 = 195/3 - 70/3 = 125/3

Answer 3

You have to write the sentences as algebra equations

solve the equations

 

x+y = 65

2x-y = 5