Question

The sum of two numbers is 14 and their difference is 2 find the numbers

Answer 1

Step-by-step explanation:

Given:-

Sum of 2 numbers=14

difference of the numbers=2

To find:-

The numbers

Solution:-

Let

the two numbers be x and y

ATQ,

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x+y=14\dots\dots(1)$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x-y=2\dots\dots (2)$

• By adding both equations

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x+y+x-y=14+2$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x+x+y-y=16$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow 2x=16$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x=\dfrac {16}{2}$

$\\\qquad\quad\displaystyle\bf {:}\longrightarrow x=8$

• Substitute the value in eq (1)

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x+y=14$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow 8+y=14$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow y=14-8$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow y=6$

$\\\\\therefore\sf The \;numbers\:are\:8\:and\:6.$

Answer 2

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