Question

Solve the following systems of equations:
2/(3x + 2y) + 3/(3x – 2y) = 17/5
5/(3x + 2y) + 1/(3x – 2y) = 2

Answer 1

Answer:

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Answer 2

x = 1, y = 1

Step-by-step explanation:

Given linear equations are:

2/(3x + 2y) + 3/(3x – 2y) = 17/5

5/(3x + 2y) + 1/(3x – 2y) = 2

Let 1/(3x + 2y) = u and 1/(3x - 2y) = v, we get:

2u + 3v = 17/5

10u + 15v = 17-------------(1)

5u + v = 2 -------------(2)

(2)*15 will be 75u + 15v = 30 -----------(3)

Subtracting (3) from (1), we get: -65u = -13

Therefore u = +1/5

Substituting in u = 1/5 equation 1, we get 2 + 15v = 17

v = +1

u = 1/(3x + 2y) = 1/5, so we get 3x + 2y = 5 ----------------(4)

v = 1/(3x - 2y) = 1  , so we get 3x - 2y = 1 ---------------(5)

Adding 4 & 5, we get: 6x = 6.

Therefore x = 1.

Substituting x = 1 in equation 4, we get: 3 + 2y = 5

Therefore y = 2/2 = 1.

Hence solved. x = 1, y = 1