[tex]49x – 57y = 172 and 57x – 49y = 252[/tex]
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2 thoughts on “<br />[tex]49x – 57y = 172 and 57x – 49y = 252[/tex]<br />​”

1. Topic :–

   • Linear Equation in Two Variable

   Given :–

   • 49x – 57y = 172 . . . .equation (1)
   • 57x – 49y = 252 . . . . equation (2)

   To Find :-

   • Value of ‘x’ and ‘y’.

   Solution :-

   Adding equation (1) and (2) :–

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

   Opening brackets,

   49x – 57y + 57x – 49y = 172 + 252

   Grouping similar terms,

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

   Solving further,

   106x + (-106y) = 424

   106x – 106y = 424

   106(x – y) = 424

   x – y = 424/106

   x – y = 4 . . . . equation (3)

   Subtracting equation (1) from (2) :–

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

   Opening brackets,

   57x – 49y – 49x + 57y = 252 – 172

   Grouping similar terms,

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

   Solving further,

   8x + 8y = 80

   8(x + y) = 80

   (x + y) = 80/8

   x + y = 10 . . . . . equation (4)

   Adding equation (3) and (4) :–

   (x – y) + (x + y) = 4 + 10

   Opening brackets,

   x – y + x + y = 4 + 10

   Grouping similar terms,

   (x + x) + (y – y) = 4 + 10

   Solving further,

   2x + 0 = 14

   x = 14/2

   x = 7

   Subtracting equation (3) from (4) :-

   (x + y) – (x – y) = 10 – 4

   Opening brackets,

   x + y – x + y = 10 – 4

   Grouping similar terms,

   (x – x) + (y + y) = 10 – 4

   Solving further,

   0 + 2y = 6

   y = 6/2

   y = 3

   Answer :–

   • x = 7
   • y = 3

   Reply

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