Question

49x-57y=172; 57x-49y=252

Answer 1

x = 7 and y = 3

Step-by-step explanation:

First we add ,

49x-57y = 172

57x-49y = 252

+.

____________

106 x - 106y = 424

divide whole equation with 106

we get,

x-y = 4. --(1)

Then we subtract,

49x-57y = 172

57x-49y = 252

- + -

___________

-8x - 8y = -80

divide whole equation with 8

we get,

- x - y = -10.

x + y = 10

solve equation (1) and (2)

x - y = 4

x + y = 10

________

2x = 14

x = 7

substitute the value of y in equation (1)

7 - y = 4

-y = 4 -7

y = 3

Answer 2

Answer:

49x – 57y = 172 .....(I)

57x – 49y = 252 .....(II)

Adding (I) and (II)

49x+57x-57y-49y=172+252

⇒106x-106y=424

⇒x-y=4 .....(III)

Subtracting (II) from (I) we have

49x-57y-57y-(-49y)=252-172

⇒-8x-8y=-80

⇒-x-y=-10

⇒x+y=10 .....(IV)

Adding (III) and (IV)

x-y=4x+y=10⇒2x=14⇒x=7

Putting the value of x = 7 in (IV) we get

7+y=10⇒y=10-7⇒y=3

Thus, (x, y) = (7, 3).