Question

if 19x +21 y =172 and 21x +19y=228 what is the value of (x+y)

Answer 1

Answer :-

x + y = 10

Given :-

19x + 21y = 172

21x + 19y = 228

To find :-

The value of ( x + y).

Solution:-

$19x + 21 y = 172----1$

$21x +19y = 228------2$

Adding equation 1.and 2.

→$19x + 21 x + 21y +19y = 172 + 228$

→$40x + 40y = 400$

Dividing both side by 40 ,

→$\dfrac{40x}{40}+\dfrac{40y}{40}=\dfrac{400}{40}$

→$x + y = 10 ----3$

Now,

Subtract equation 1. and 2.

→$19x -21y + 21y -19y = 172-228$

→$-2x +2y = -57----4$

Multiply eq.3 with 2

→$(x+y = 10 )× 2$

→$2x +2y = 20 ---3$

Add eq.3 and 4

→$2x -2x +2y+2y = -57+20$

→$4y = -37$

→$y = \dfrac{-37}{4}$

Put the value in equation.3

$x + y = 10 \\ x -\dfrac{37}{4}= 10\\x = 10 + \dfrac{37}{4}\\ x = \dfrac{40+37}{4}\\ x = \dfrac{77}{4}$

Now,

$x + y \\ \dfrac{77}{4}-\dfrac{-37}{4}\\ x+y = \dfrac{77-37}{4}$

→$x+y = \dfrac{40}{4}$

→$x+y = 10$

hence,

The value of x+y is 10