Question

Solve 49x-57y=172 ;57x-49y=252​

Answer 1

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).

Answer 2

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• 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).