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Question

Which of the following is the solution set for the simultaneous equation ?
2x13=y+65=3xy7
  1. x=1;y=2
  2. x=2;y=1
  3. x=3;y=1
  4. x=4;y=1

A
x=1;y=2
B
x=3;y=1
C
x=2;y=1
D
x=4;y=1
Solution
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Given : 2x13=y+65=3xy7

Take two equalities simultaneously we get

2x13=y+65 and y+65=3xy7

10x5=3y+18 and 7y+42=15x5y

10x3y=23 .......... (1) and 15x12y=42 .......... (2)

from eq(2) we can get the value of x in terms of y i.e, x=42+12y15

now simply substitute this x value in eq(1) from where we can calculate the value of y and then substitute the y in any eq we can find the value of x , so

Solving (1) and (2) simultaneously we get
x=2

Substituting x in (1) we get y=1.
Hence, x=2;y=1.

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