Question

(y+2)/6 - 1/(y+2) = 1/6. So what do s the solution set of this question

Answer 1

Answer:

1) x/7 + y/3 = 5    x/2 - y/9 = 6

On taking LCM of denominators and simplifying, we get the linear equations as

3x + 7y = 105 → (1)

9x − 2y = 108 → (2)

Multiply equation(1) with 3 , we get

9x + 21y = 315 → (3)

Now subtract (2) from (3)

9x + 21y = 315

9x − 2y = 108

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23y = 207

∴ y = (207/23) = 9

Put y = 9 in 3x + 7y = 105

3x + 7(9) = 105

⇒ 3x = 105 − 63 = 42

∴ x = (42/3) = 14

2) 4x + 6/y = 15

   3x - 4/y = 7

put (1/y) = p

Hence the above equations become,

4x + 6p =15 → (1)

3x − 4p = 7 → (2)

Multiply equation (1) with 4 and equation (2) with 6 and add as shown

16x + 24p = 60

18x − 24p = 42

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34x = 102

∴ x = (102/34) = 3

Put x = 3 in 4x + 6p =15

4(3) + 6p = 15

12 + 6p = 15

6p = 3

∴  p = (3/6) = (1/2)

⇒ (1/y) = (1/2)

∴ y = 2

Answer 2

Solve the following system of linear equations by elimination-method

2/x + 2/3y = 1/6 , 3/x + 2/y = 0

Solution:

2/x + 2/3y = 1/6 ---- (1)

3/x + 2/y = 0 ---- (2)

Let 1/x = a and 1/y = b

2 a + (2b/3) = 1/6

(6 a + 2 b)/3 = 1/6

6 (6 a + 2 b ) = 3

36 a + 12 b = 3

Dividing the whole equation by 3 we get

12 a + 4 b = 1 ------- (1)

3 a + 2 b = 0 ---------(2)

12 a + 4 b = 1

There are two unknowns in the given equations. By solving these equations we have to find the values of a and b. For that let us consider the coefficients of a and b in both equation. In the first equation we have + 4b and in the second equation also we have + 2b and the symbols are same so we have to subtract them for eliminating the variable b.

Multiply the second equation by 2 => 6 a + 4 b = 0

Subtracting the second equation from the first equation

12 a + 4 b = 1

6 a + 4 b = 0

(-) (-) (-)

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6 a = 1

a = 1/6

now we have to apply the value of a in either given equations to get the value of another variable b

Substitute a = 1/6 in the first equation we get

12(1/6) + 4 b = 1

2 + 4 b = 1

4 b = 1- 2

4 b = -1

b = -1/4

Solution:

x = 6

y = -4

verification:

2/x + 2/3y = 1/6

2/6 + 2/3(-4) = 1/6

1/3 -1/6 = 1/6

1/6 = 1/6

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