Question

49x -57y =172 ; 57x - 49y =252​

Answer 1

Given equations

$49x-57y = 172 --(1)\\57x-49y=252--(2)$

Adding (1) and (2), we get,

$49x-57y+57x-49y=172+252\\\implies 106x-106y= 424\\\implies 106(x-y) = 424$

$\implies x-y = \dfrac{424}{106}$

$\implies x-y = 6--(3)$

Subtracting (3) and (4), we get,

$49x-57y-57x+49y=172-252\\\implies -8x-8y = -80\\\implies 8x+8y=80\\\implies 8(x+y)=80$

$\implies (x+y) = \dfrac{80}{8}$

$\implies x+y=10--(4)$

Solving eq, (3) and (4), we get,

$x-y=6\\\underline{x+y=10}\\\underline{\underline{2x=16}}\\\implies x = 8\\\implies y = 2$

$\boxed{\boxed{\bold{Therefore, \ the \ values \ of \ x \ and \ y \ are \ 8 \ and \ 2 \ respectively}}}}}}$

                                                                     

Answer 2

Answer:

Given :-

49x - 57y = 172 ........(i), and

57x-49y=252.............(ii)

Adding (i) and (ii), we get

106x - 106y = 424

=> x - y = 4 .................(iii)

Now substracting (i) and (ii), we get

-8x - 8y = -80

=> x + y = 10 ...............(iv)

Adding (iii) and (iv), we get

2x = 14

=> x = 7

putting the value of x in question (iii), we get

y = 3

hope you like this

please mark me as brainlist