Solve for x and y:
217x + 131y = 913 and 131x + 217y = 827

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x=3, y=2

x=8,y=9

x=5, y=6

x=3, y=6

answer is C.

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Detailed Solution

The given pair of equations are

217 x + 131 y = 913

and

131 x + 217 y = 827

.
Adding the given equations to obtain simplified equations,

⇒ 217 x + 131 y + 131 x + 217 y = 913 + 827 ⇒ 348 x + 348 y = 1740 ⇒ x + y = 5... (1)

Subtracting the equations,

217 x + 131 y = 913

and

131 x + 217 y = 827

⇒ 217 x + 131 y − 131 x − 217 y = 913 − 827 ⇒ 86 x − 86 y = 86 ⇒ x − y = 1... (2)

Adding equations 1 and 2 and solving for x,

⇒ x + y + x − y = 6 ⇒ 2 x = 6 ⇒ x = 3

Using the value of x in equation (2) to find the value of y,

⇒ 3 − y = 1 ⇒ y = 2

Therefore, the values of x and y are 3 and 2 respectively.
Hence, the correct option is 3.

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