Question

The sum of twice a number and another number is 24. The difference of twice the first number and the other number is 12. Which system would model this situation, and what is the solution?

Answer 1

The system that models the situation is:

`\left \{{{2x + y = 24} \atop {2x - y = 12}} \right.`

The solution is:

(9, 6)

Explanation:

We must write the equations as indicated in the problem.

The sum of twice a number and another number is 24

a number: x

other number: y

Then

`2x + y = 24`

The difference of twice the first number and the other number is 12

first number: x

other number: y

Then:

`2x - y = 12`

The system that models the situation is:

`\left \{{{2x + y = 24} \atop {2x - y = 12}} \right.`

To solve the system we add both equations to find the value of x

`2x + y = 24\\\\2x - y = 12`

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

`4x +0 = 36\\\\x=(36)/(4)\\\\x=9`

`2(9) +y = 24\\\\y=24-18\\\\y=6`

The solution is:

(9, 6)