Advertisements
Advertisements
प्रश्न
Solve the following pair of linear equations.
`x/a-y/b = 0`
ax + by = a2 + b2
उत्तर
`x/a-y/b = 0`
Or, bx − ay = 0 … (1)
ax + by = a2 + b2 … (2)
Multiplying equation (1) and (2) by b and a respectively, we obtain
b2x − aby = 0 … (3)
a2x + aby = a3 + ab2 … (4)
Adding equations (3) and (4), we obtain
b2x + a2x = a3 + ab2
x (b2 + a2) = a (a2 + b2)
x = a
By using (1), we obtain
b (a) − ay = 0
ab − ay = 0
ay = ab
y = b
APPEARS IN
संबंधित प्रश्न
Solve `\frac { 2 }{ x } + \frac { 1 }{ 3y } = \frac { 1}{ 5 }; \frac { 3 }{ x } + \frac { 2 }{ 3y } = 2` and also find ‘a’ for which y = ax – 2
Solve the following systems of equations
(i)`\frac{15}{u} + \frac{2}{v} = 17`
`\frac{1}{u} + \frac{1}{v} = \frac{36}{5}`
(ii) ` \frac{11}{v} – \frac{7}{u} = 1`
`\frac{9}{v} + \frac{4}{u} = 6`
Formulate the following problems as a pair of equations, and hence find their solutions:
Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju
Solve the following pair of linear equations.
(a − b) x + (a + b) y = a2− 2ab − b2
(a + b) (x + y) = a2 + b2
In Fig. 1, ABCD is a rectangle. Find the value of x and y.
A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?
A two-digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places. Find the number.
A father is three times as old as his son. After twelve years, his age will be twice as that of his son then. Find the their present ages.
Asha has only ₹1 and ₹2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ₹75, then the number of ₹1 and ₹2 coins are, respectively.
