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Find the solution of the pair of equations $x 10 + y 5 − 1 = 0 a n d x 8 + y 6 = 15.$ Hence, find $λ$ Hence, find , if $y = λ x + 5$ , if .

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the solution of the pair of equation is

x = 140, y = − 165

and the value of

λ

− 1 2

the solution of the pair of equation is

x = 240, y = − 165

and the value of

λ

− 1 2

the solution of the pair of equation is

x = 340, y = − 150

and the value of

λ

− 1 2

the solution of the pair of equation is

x = 340, y = − 165

and the value of

λ

− 1 2

answer is D.

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Detailed Solution

Given equations are

x 10 + y 5 − 1 = 0

……………….(1)

x 8 + y 6 = 15

……………..(2)
We know if two fractions are supplied with distinct denominators, multiply one fraction by the denominator of the other in both the numerator and the denominator.
Solve equation (1).

x 10 + y 5 − 1 = 0

x 10 + y 5 × 22 − 1 × 1010 = 0

x 10 + 2 y 10 − 1010 = 0

x + 2 y − 10 10 = 0

x + 2 y − 10 = 0

……………(3)
Now, solve equation (2).

x 8 + y 6 − 15 = 0

x 8 × 66 + y 6 × 88 − 15 × 66 × 88 = 0

6 x 48 + 8 y 48 − 15 × 4848 = 0

6 x 48 + 8 y 48 − 72048 = 0

3 x 24 + 4 y 24 − 36024 = 0

3 x + 4 y − 360 = 0

………………(4)
Multiply equation (3) by 3.

3 x + 6 y − 30 = 0

……………(5)
Subtract equation (5) by (4).

3 x + 6 y − 30 − 3 x + 4 y − 360 = 0 = 0

3 x + 6 y − 30 − 3 x − 4 y + 360 = 0

6 y − 30 − 4 y + 360 = 0

2 y + 330 = 0

2 y = − 330

y = − 330 2

y = − 165

Substitute the value of y = -165 in equation (5).

3 x + 6 − 165 − 30 = 0

3 x − 990 − 30 = 0

3 x = 1020

x = 10203

x = 340

Given that the relation between x, y and

λ

y = λ x + 5

.
Substitute values of x= 340 and y= -165 in above equation.

− 165 = λ 340 + 5

λ 340 = − 165 − 5

λ 340 = − 170

λ = − 170 340

λ = − 1 2

Hence, the solution of the pair of equation is

x = 340, y = − 165

and the value of

λ

− 1 2

.
The correct option is (4).

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Find the solution of the pair of equations x 10 + y 5 −1=0 and x 8 + y 6 =15. Hence, find λ Hence, find , if y=λx+5 , if .

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Find the solution of the pair of equations $x 10 + y 5 − 1 = 0 a n d x 8 + y 6 = 15.$ Hence, find $λ$ Hence, find , if $y = λ x + 5$ , if .