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# Solve the Following Systems of Equations: 5/(X + 1) - 2/(Y -1) = 1/2 10/(X + 1) + 2/(Y - 1) = 5/2 Where X != -1 and Y != 1 - CBSE Class 10 - Mathematics

ConceptAlgebraic Methods of Solving a Pair of Linear Equations Substitution Method

#### Question

Solve the following systems of equations:

5/(x + 1) - 2/(y -1) = 1/2

10/(x + 1) + 2/(y - 1) = 5/2 where x != -1 and y != 1

#### Solution

Let 1/(x + 1) = u and 1/(y - 1) = v

Then, the given system of equations becomes

=> 5u - 2v = 1/2 .....(i)

=> 10u + 2y = 5/2 ....(2)

Adding equation (i) equation (ii), we get

5u + 10u = 1/2 + 5/2

=> 15u = (1 + 5)/2

=> 15u = 6/2 = 3

=> u = 3/15 = 1/5

Putting u = 1/5 in equation (i)  we get

5 xx 1/5 - 2v = 1/2

=> 1 - 2v = 1/2

=> -2v = 1/2 - 1

=> -2v = (1 - 2)/2

=> -2v = (-1)/2

=> v = (-1)/(-4) = 1/4

Now u = 1/(x + 1)

=> 1/(x + 1) = 1/5

=> x + 1 = 5

=> x = 5 -1 =4

And v = 1/(y - 1)

=> 1/(y -1) = 1/4

=> y - 1 = 4

=> y = 4 + 1 = 5

Hence, solution of the give system of equation is x = 4, y = 5

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Solution Solve the Following Systems of Equations: 5/(X + 1) - 2/(Y -1) = 1/2 10/(X + 1) + 2/(Y - 1) = 5/2 Where X != -1 and Y != 1 Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method.
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