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Two numbers have a sum of 23 and a difference of 9 find the 2 numbers

User Jeanfrg
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1 Answer

5 votes

SOLUTION

Define a variable for the unknown numbers.


\text{ let the numbers be x and y}

The sum is 23, implies


x+y=23

The difference is 9 is written as


x-y=9

Then we have the system of equation


\begin{gathered} x+y=23\ldots\text{equation}1 \\ x-y=9\ldots\text{equation}2 \end{gathered}

Add equation 1 and 2.


\begin{gathered} 2x-0=32 \\ 2x=32 \end{gathered}

Divide both sides by 2


\begin{gathered} (2x)/(2)=(32)/(2) \\ \text{Then} \\ x=16 \end{gathered}

hence x=16

Recall equation 1


\begin{gathered} x+y=23 \\ \text{ put x=16} \\ 16+y=23 \end{gathered}

Subtract 16 from both sides, we have


\begin{gathered} 16-16+y=23-16 \\ y=7 \end{gathered}

Hence, y=7

Answer: The numbers are 16 and 7

User Chance
by
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