Question

49x - 57y = 172; 57x - 49y = 252​

Answer 1

Answer:

49x - 57y = 172

57x - 49y = 252

49x = 172 + 57y

x = 172+57y/48 ....................(1)

57 * 172+57y / 48 - 49y = 252

19*172+57y/16 -49y =252

3268+1083y/16 -49y = 252

3268+1083y - 784y/16=252

3268+299y = 252 * 16

3268 + 299y = 4032

299y = 4032-3268

299y= 764

y = 764/299

y= 2.5

put value of y in equation (1)

x= 172 + 57(2.5)/48

x= 146

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).