Question

The sum of two numbers is equal to 11 and the difference is 19. What are the two numbers?

Answer 1

`\bold{\huge{\pink{\underline{ Solution }}}}`

We have given in the question that,

• The sum of 2 numbers is equal to 11
• The difference between two numbers is 19 .

`\bold{\underline{ To \: Find }}`

• We have to find the value of x and y.

`\bold{\underline{ Let's \: Begin }}`

Let the two numbers be x and y

According to the question,

`\sf{ x + y = 11......eq(1) }`

`\sf{ x - y = 19......eq(2) }`

Solving eq( 1 ) we get :-

`\sf{ x + y = 11 }`

`\sf{ x = 11 - y ......eq(3 ) }`

Subsituting eq(3 ) in eq(2) :-

`\sf{ x - y = 19 }`

`\sf{ ( 11 - y) - y = 19 }`

`\sf{ 11 - y - y = 19 }`

`\sf{ 11 - 2y = 19 }`

`\sf{ - 2y = 19 - 11 }`

`\sf{ - 2y = 8}`

`\sf{ y = 8/(-2) }`

`\sf{ y = - 4 }`

`\sf{\red{Thus ,\: the\: value\: of \: y = -4}}`

Now, Subsitute the value of y in eq( 3 ) :-

`\sf{ x = 11 - y }`

`\sf{ x = 11 - (-4 ) }`

`\sf{ x = 11 + 4 }`

`\sf{ x = 15 }`

Hence, The value of x and y are 15 and (-4) .