Question

the sum of two numbers is 14 their difference is 6

Answer 1

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Answer 2

Let the numbers be 'x' and 'y'.

Now according to the question,

x+y=14.................(i)

x-y=6....................(ii)

Adding equation (i) and (ii),

$\: \: \: \: \: \: \: \: \: x + y + x - y = 14 + 6 \\ = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x = 20 \\ = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{20}{2} \\ = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 10$

Substituting the value of x in equation (i)

$\: \: \: \: \: \: \ \: : x + y = 14 \\ = > 10 + y = 14 \\ = > \: \: \: \: \: \: \: \: \: y = 14 - 10 \\ = > \: \: \: \: \: \: \: \: \: y = 4$

So,

$\huge{\boxed{x=10 \: and \: y=4}}$