Question

The sum of two numbers is 7 and their diffrence is 1

Answer 1

$\huge\bf\underline{\red{Solution:-}}$

$\sf\bullet Sum\:of\:two\: numbers= 7\\ \\ \sf\bullet their\: difference=1\\ \\ \sf\:\:\:\:let\:the\: number\:be\:a\:and\:b\\ \\ \sf\implies a+b=7......\:\:\:(1)\\ \\ \sf\implies a-b=1..........(2)$

$\bf\underline{\red{A.T.Q:-}}$

$\sf:\:\:\:Add\: equation\:1\:\:and\:\:2\\ \\ \sf\implies a+b+(a-b)= 7+1\\ \\ \sf\implies a+\cancel{b}+a\cancel{-b}=8\\ \\ \sf\implies 2a=8\\ \\ \sf\implies a=\cancel{\dfrac{8}{2}}\\ \\ \sf\implies a=4\\ \\ \sf\:\:\:{\blue{\:\:\:\:\:Now\:the\: numbers}}\\ \\ \sf\leadsto a+b=7\\ \\ \sf\leadsto 4+b=7\\ \\ \sf\leadsto b=7-4\\ \\ \sf\implies b=3$

$\underline{\dag{\sf{\:The\:two\: numbers=4\:and\:3}}}$

Answer 2

Answer:

$\large{\underline{\boxed{\mathfrak\green{Two \: numbers \: are = 3 \: and \: 4}}}}$

$\rule{100}{1}$

Correct question:-

The sum of two numbers is 7 and their difference is 1.Find the numbers.

Given:-

• Sum of numbers = 7
• Difference b/w numbers = 1

To find:-

• Numbers = ?

Let the numbers be x & y respectively.

A/Q,

1st case:-

$\dashrightarrow\sf x + y = 7 \\\\\\\dashrightarrow\sf x = 7 - y \dots\dots (eq.1)$

2nd case:-

$\dashrightarrow\sf x - y = 1 \\\\\\\dashrightarrow\sf x = y + 1 \\\\\\\scriptsize\sf\green{\: \: \: \: [From \: (eq.1) \: :- ]}\\\\\\\dashrightarrow\sf 7 - y = y + 1 \\\\\\\dashrightarrow\sf - y - y = 1 - 7 \\\\\\\dashrightarrow\sf - 2y = - 6 \\\\\\\dashrightarrow\sf y = -6/-2 \\\\\\\dashrightarrow\large{\underline{\boxed{\sf\green{y = 3}}}}$

$\rule{100}{2}$

• Putting value of y in (eq.1) :-

$\dashrightarrow\sf x = 7 - 3 \\\\\\\dashrightarrow\large{\underline{\boxed{\sf\blue{x = 4}}}}$

$\therefore{\underline{\underline{\sf\pink{Numbers = 3 \: \& \: 4 }}}}$