Question

Solve the following systems of equations :
44/(x + y) + 30/(x – y) = 10
55/(x + y) + 40/(x – y) = 13

Answer 1

Answer:

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Answer 2

x = 8, y = 3

Step-by-step explanation:

Given linear equations are:

44/(x + y) + 30/(x – y) = 10

55/(x + y) + 40/(x – y) = 13

Let 1/x+y = u and 1/x-y = v, we get:

44u +30v = 10-------------(1)

55u + 40v = 13-------------(2)

(1)*4 will be 176u + 120v = 40

(2)*3 will be 165u + 120v = 39

Subtracting, we get: 11u = 1

Therefore u = 1/11

Substituting in equation 1, we get 4 +30v = 10

v = 6/30 = 1/5

1/x+y = 1/11

So x+y = 11 -----------(3)

1/x-y = 1/5

So x-y = 5 -----------(4)

Adding 3 & 4, we get:

2x = 16

x = 8

Substituting in equation 3, we get 8 + y = 11

y = 3

Hence solved. x = 8, y = 3