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# Solve the Following Systems of Equations: 22/(X + Y) + 15/(X - Y) = 5 55/(X + Y) + 45/(X - Y) = 14 - CBSE Class 10 - Mathematics

ConceptAlgebraic Methods of Solving a Pair of Linear Equations Substitution Method

#### Question

Solve the following systems of equations:

22/(x + y) + 15/(x - y) = 5

55/(x + y) + 45/(x - y) = 14

#### Solution

Let 1/(x + y) = u and 1/(x - y) = v Then, the given system of equation becomes

22u + 15v = 5 ...(i)

55u + 45v = 14..(ii)

Multiplying equation (i) by 3, and equation (ii) by 1, we get

66u + 45v = 15 ....(iii)

55u + 45v = 14 .....(iv)

Subtracting equation (iv) from equation (iii), we get

66u - 55u = 15 - 4

=> 11u = 1

=> u = 1/11

Putting u = 1/11 in equaiton (i) we get

22 xx 1/11 + 15v = 5

=> 2 + 15v = 5

=> 15v = 5 - 2

=> 15v = 3

=> v = 3/5 = 1/5

Now u = 1/(x + y)

=> 1/(x + y) = 1/11

=> x + y = 11 ....(v)

And v = 1/(x - y)

=> 1/(x- y) = 1/5

=> x - y = 5  .....(vi)

Adding equation (v) and equation (vi), we get

2x = 11 + 5

=> 2x = 16

=> x = 16/2 = 8

Putting x =- 8 in equation (v), we get

8 + y = 11

y = 11 - 8 = 3

Hence, solution of the given system of equation is x = 8, y = 3

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Solution Solve the Following Systems of Equations: 22/(X + Y) + 15/(X - Y) = 5 55/(X + Y) + 45/(X - Y) = 14 Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method.
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