Question

The sum of two numbers is 20 and the difference is 12. What are the numbers?

1. Create a system of two linear equations to represent this problem.
2. Solve the system to find the 2 numbers

Answer 1

1) A system of two linear equations to represent this problem

x+y=20 and x-y=12

2) The numbers are x=16 and y=4

Explanation:

Let x and y be the two numbers

Given that the sum of the two numbers is 20

That is
`x+y=20\hfill (1)`

and the difference is 12

That is
`x-y=12\hfill (2)`

1) A system of two linear equations to represent this problem

`x+y=20\hfill (1)`

`x-y=12\hfill (2)`

2). Noe Solve the system to find the 2 numbers:

Adding the equations (1) and (2) we get

`x+y=20`

`x-y=12`

_____________

2x=32

`x=(32)/(2)`

Therfore x=16

Now substitute x=16 in equation (1) we get

`16+y=20`

`y=20-16`

Therefore y=4

Therefore the numbers are x=16 and y=4