Question

If 19x + 17y = 55, 17x + 19y = 53, then the value of (x + y) is ………………….

Answer 1

Step-by-step explanation:

(19x - 17y) +(17x-19y) =55 + 53

36x - 36y = 108

x-y=3.....(1)

now,

(19x - 17y) - (17x-19y) =55 - 53

2x + 2y =2

x+y=1....(2)

from (1)+(2)=>2x=4

=>x=2

therefore y =-1 ....(from 1)

Answer 2

The value of (x + y) is 3.

Explanation:

The given equations :

$19x + 17y = 55 -----------------(1)\\\\ 17x + 19y = 53------------------(2)$

Multiply 19 on both sides of equation (1) , we get

$19(19x + 17y) =19( 55)\\\\ 361x+323y=1045-------------------(3)$

Similarly , Multiply 17 on both sides of equation (2) , we get

$289x + 323y = 901------------------------------(4)$

Subtract (3) from (4), we get

$72x=144\Rightarrow\ x=\dfrac{144}{72}=2$

∴ $x= 2$

Put x=2 in (1) , we get

$19(2) + 17y = 55$

$38 + 17y = 55$

$17y =55-38=17$

∴$y=1$

Then , $x+y=2+1=3$

Hence, the value of (x + y) is 3.

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