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प्रश्न
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.
उत्तर
Given pair of equations is
`x/10 + y/5 - 1` = 0
⇒ x + 2y – 10 = 0 ......(i)
⇒ x + 2y = 10
And `x/8 + y/6` = 15
⇒ 3x + 4y = 360 ......(ii)
On multiplying equation (i) by 2 and then subtracting from equation (ii), we get
(3x + 4y) – (2x + 4y) = 360 – 20
⇒ x = 340
Put the value of x in equation (i), we get
340 + 2y = 10
⇒ 2y = 10 – 340 = –330
⇒ y = –165
Now, y = λx + 5
Put the values of x and y in above relation, we get
–165 = λ(340) + 5
⇒ 340λ = –170
⇒ λ = `- 1/2`
Hence, the solution of the pair of equations are x = 340, y = –165 and the required value of λ is `- 1/2`.
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