a first number plus twice a second number is 10. twice the first number plus the second number is 17 . What is the smaller and larger number

Question

Must find the larger and the smaller number that gives the answer to the two equations. 

Answer 1

Let the first number = x

Let the second number = y

 

We can set to equations based on the information given using the above variables.

 

x + 2y = 10         eq1

2x + y = 17         eq2

 

We have a system of equations. 

 

First multiply eq1 by 2.

 

2x + 4y = 20        eq1

2x + y = 17          eq2

 

Subtract eq2 from eq1 to eliminate the x terms.  This will allow us to solve for y.

 

3y = 3

  y = 1

 

 

Now, substitute this value of y into eq1 to solve for x

 

x + 2y = 10

x + 2(1) = 10

x + 2 = 10

x = 8

 

The smaller number is 1.

The larger number is 8.