Advertisements
Advertisements
Question
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
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`.
APPEARS IN
RELATED QUESTIONS
A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.
Solve the following systems of equations:
`x + 2y = 3/2`
`2x + y = 3/2`
Solve the following systems of equations:
`3x - (y + 7)/11 + 2 = 10`
`2y + (x + 10)/7 = 10`
Solve the system of equations by using the method of cross multiplication:
3x - 2y + 3 = 0,
4x + 3y – 47 = 0
Solve the system of equations by using the method of cross multiplication:
`1/x + 1/y = 7, 2/x + 3/y = 17`
A father's age is three times the sum of the ages of his two children. After 5 years his age will be two times the sum of their ages. Find the present age of the father.
Complete the activity to find the value of x.
3x + 2y = 11 …(i) and 2x + 3y = 4 …(ii)
Solution:
Multiply equation (i) by _______ and equation (ii) by _______.
`square` × (3x + 2y = 11) ∴ 9x + 6y = 33 …(iii)
`square` × (2x + 3y = 4) ∴ 4x + 6y = 8 …(iv)
Subtract (iv) from (iii),
`square` x = 25
∴ x = `square`
Solve 0.4x + 0.3y = 1.7; 0.7 x − 0.2y = 0.8
A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.
A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. Find the cost price of the saree and the list price (price before discount) of the sweater.
