Question

5. The sum of two numbers is 24. The second number is 4 less than the first. Write a system of equations andsolve it to find the numbers.A. (16,8)B. (14, 10)C (18, 14)D (6,4)

Answer 1

Take x and y as the two numbers, the sum of these is 24:

`x+y=24`

It is also stated that the second number, y, is 4 less than the first, x, it means:

`y=x-4`

The system of equations is:

`\begin{gathered} x+y=24 \\ y=x-4 \end{gathered}`

Use the second equation, which is solved for y and replace this expression for y in the first equation, then solve for x:

`\begin{gathered} x+y=24 \\ x+(x-4)=24 \\ x+x-4=24 \\ 2x=24+4 \\ 2x=28 \\ x=(28)/(2) \\ x=14 \end{gathered}`

x has a value of 14. Use this value and the second equation to find the value of y:

`\begin{gathered} y=x-4 \\ y=14-4 \\ y=10 \end{gathered}`

The solution for the system is (14,10). The correct answer is B.