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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, if y = λx + 5

Solution:

From the above question, we have the equation as,

x/10 + y/5 - 1 = 0-----------(1)

x/8 + y/6 = 15-----------------(2)

Rearranging the equation, we get,

x + 2y = 10-----------------(3)

3x + 4y = 360--------------(4)

Multiplying (3) by 2 and by subtracting from (4),

(3x + 4y) - (2x + 4y) = 360 - 20

x = 340.

Substitute the value of x in (3),

340 + 2y = 10

2y = 10 - 340 = -330

y = -165.

We have, y = λx + 5.

Substituting the x and y value in above equation,

-165 = λ(340) + 5

340λ = -170

λ = -1/2.

x = 340.

y = -165.

λ = -1/2.

Therefore, the solutions of the pair of equations are x = 340, y = -165 and the required value of λ is -1/2.

✦ Try This: Find the solution of the pair of equations x/10 + y/5 - 2 = 0 and x/8 + y/6 = 15. Hence, find λ, if y = λx + 5

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 10

Summary:

The solutions of the pair of equations x/10 + y/5 - 1 = 0 and x/8 + y/6 = 15 are x = 340, y = -165. λ, if y = λx + 5 is -1/2

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