Question

find X and Y 5 by X + Y - 2 by x minus y equal to minus 1 and 15 by X + Y + 7 by x minus 5 equal to 10​

Answer 1

Solution :-

$\sf \dfrac{5}{x + y} - \dfrac{2}{x - y} = - 1 \\ \\ \\ \sf \dfrac{15}{x + y} + \dfrac{7}{x - y} = 10$

Reducing the above equations into pair of linear equations

$\tt \underline{it \: can \: be \: written \: as} \\ \\ \\ \sf 5 \bigg(\frac{1}{x + y} \bigg) - 2 \bigg( \dfrac{1}{x - y} \bigg) = - 1\\ \\ \\ \sf 15 \bigg( \dfrac{1}{x + y} \bigg) + 7 \bigg( \dfrac{1}{x - y} \bigg) = 10$

Substitute 1/(x + y) = a and 1/(x - y) = b in above pair of linear linear eqations:

5a - 2b = - 1 -----eq(1)

15a + 7b = 10 ---eq(2)

Coefficients of b are 2 and 7 and their LCM is 14

Equation (1) * 7 : 35a - 14b = - 7 ---eq(3)

Equation (2) * 2 : 30a + 14b = 20 ---eq(4)

Adding (1) and (2)

35a - 14b + (30a + 14b) = - 7 + 20

35a - 14b + 30a + 14b = 13

35a + 30a = 13

65a = 13

a = 13/65

a = 1/5

Substitue a = 1/5 in eq(1)

$\sf 5a - 2b = - 1 \\ \\ \\ \sf 5 \bigg( \dfrac{1}{5} \bigg) - 2b = - 1$

1 - 2b = - 1

1 + 1 = 2b

2 = 2b

2/2 = b

1 = b

b = 1

But, 1/(x + y) = a

1/(x + y) = 1/5

x + y = 5 ---eq(5)

1/(x - y) = 1

x - y = 1 ---eq(6)

Adding (5) and (6)

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

x + y + x - y = 6

2x = 6

x = 6/2

x = 3

Substitute x = 3 in eq(5)

x + y = 5

3 + y = 5

y = 5 - 3

y = 2

Answer 2

Answer:

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Step-by-step explanation:

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