Question

5. The sum of two numbers is 56. The difference of the two numbers is 9. What is theproduct of the two numbers?What are you being asked to find?What are you given?Define your variables.?Create & solve a system.Explain your solution.

Answer 1

Define your variable:

Let x and y be two numbers.

What are you given?

We know that,

`\begin{gathered} x+y=56 \\ \text{and} \\ x-y=9 \end{gathered}`

Create and solve a system.

The system is

`\begin{gathered} x+y=56 \\ x-y=9 \end{gathered}`

Explain your solution.

We can solve this systemn by elimination method. If we add both equation, we obtain

`x+x=56+9`

because y-y=0. Then, we have

`\begin{gathered} 2x=65 \\ x=(65)/(2) \\ x=32.5 \end{gathered}`

Now, we must substitute this value into the first equation. It yields,

`\begin{gathered} 32.5+y=56 \\ y=56-32.5 \\ y=23.5 \end{gathered}`

Therefore, the answer is x=32.5 and y=23.5