Question

49x-57y=172, 57x-49y=252​

Answer 1

Step-by-step explanation:

$\sf \purple{ \clubs \: Given :} \\ \bigg \lgroup { 49x-57y=172 }\bigg \rgroup \\\bigg \lgroup{ 57x-49y=252}\bigg \rgroup \\ \sf \purple{ \clubs \: To \: find :} \\ \dag \sf \: Value \: of \: x \: and \: y \: . \\ \sf \purple{ \clubs \: Solution :} \\ \sf By \: using \: substitution \: method \\ \sf \: 49x -57y = 172 \longrightarrow (1)\\ \sf 49x = 172 + 57y \\ \sf x = \frac{172 + 57y}{49} \longrightarrow (2) \\ \sf \: 57x-49y=252 \longrightarrow \:Given \\ \sf \: Putting \: value \: from \: (2) \: in \: above \: equation \\ \sf 57(\frac{172 + 57y}{49}) - 49y = 252 \\ \sf \: \frac{9804 + 3249y}{49} - 49y = 252 \\ \sf \: \frac{9804 + 3249y - 2401y}{49} = 252 \\ \sf \: 9804 + 848y = 49 \times 252 \\ \sf \: 9804 + 848y = 12348 \\ \sf \: 848y = 12348 - 9804 \\ \sf \: 848y = 2544 \\ \sf \: y = \frac{2544}{848} \\ \boxed{ \sf \: y = 3} \\ \sf \: Putting \: value \: of \: y \: i n \: equation \: (2) \\ \sf \: x = \frac{172 + 57 \times 3}{49} \\ \sf x = \frac{172 + 171}{49} \\ \sf \: x = \frac{343}{49} \\ \boxed{ \sf \: x \: = 7} \\ \sf \: Which \: is \: the \: required \\ \sf \: Answer \: .$

Answer 2

Answer:

49x - 57y = 172

57x - 49y = 252

Adding 49x - 57y = 172 and 57x - 49y = 252

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

= 106x - 106y = 424

= x - y = 4

Subtract ,

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

= -8x - 8y = -80

= -x+y = 10

Adding

x - y = 4

x + y = 10

= 2x = 14

= x= 7

Putting the value of x = 7 in 10 we get

7 + y = 10

= y = 10 - 7

= y = 3

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

Hope it will help you

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