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Question
Solve the following systems of equations:
`2(1/x) + 3(1/y) = 13`
`5(1/x) - 4(1/y) = -2`
Solution
Let us write the given pair of equation as
`2(1/x) + 3(1/y) = 13` ....(1)
`5(1/x) - 4(1/y) = -2` ....(2)
These equation are not in the form ax + by + c = 0 However, if we substitute
`1/x = p` and `1/y = q` in equation (1) and (2) we get
2p + 3q = 13
5p - 4q = -2
So, we have expressed the equations as a pair of linear equations. Now, you can use any method to solve these equations, and get p = 2, q = 3
You know that `p =1/x and q =1/y`
Substitute the values of p and q to get
`1/x = 2 i.e x = 1/2 and 1/y = 3 " i.e " y = 1/3`
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