Advertisements
Advertisements
प्रश्न
Solve the following simultaneous equation.
`x/3 + y/4 = 4; x/2 - y/4 = 1`
Advertisements
उत्तर
`x/3 + y/4 = 4` ...(I)
`x/2 - y/4 = 1` ...(II)
Multiplying (I) with LCM of 3 and 4 which is 12, we get,
4x + 3y = 48 ...(III)
Multiplying (II) with LCM of 2 and 4 which is 4, we get,
2x - y = 4 ...(IV)
Multiplying (IV) with 2,
4x - 2y = 8 ...(V)
Subtracting (V) from (III)
4x + 3y = 48
4x - 2y = 8
- + -
5y = 40
⇒ y = 8
Putting this value of y in (IV) we get,
∴ 2x - y = 4
⇒ 2x - 8 = 4
⇒ 2x = 12
⇒ x = 6.
APPEARS IN
संबंधित प्रश्न
Solve the following system of linear equations by applying the method of elimination by equating the coefficients
(i)4x – 3y = 4
2x + 4y = 3
(ii)5x – 6y = 8
3x + 2y = 6
Solve the following system of linear equations by using the method of elimination by equating the coefficients: 3x + 4y = 25 ; 5x – 6y = – 9
Solve the following system of equations by using the method of elimination by equating the co-efficients.
`\frac { x }{ y } + \frac { 2y }{ 5 } + 2 = 10; \frac { 2x }{ 7 } – \frac { 5 }{ 2 } + 1 = 9`
Solve the following system of linear equations :
2(ax – by) + (a + 4b) = 0
2(bx + ay) + (b – 4a) = 0
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes `1/2` if we only add 1 to the denominator. What is the fraction?
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Sanjay gets fixed monthly income. Every year there is a certain increment in his salary. After 4 years, his monthly salary was Rs. 4500 and after 10 years his monthly salary became 5400 rupees, then find his original salary and yearly increment.
Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay's age?
Solve the following simultaneous equation.
2x + y = -2 ; 3x - y = 7
Solve the following simultaneous equation.
`x/3 + 5y = 13 ; 2x + y/2 = 19`
By equating coefficients of variables, solve the following equation.
5x + 7y = 17 ; 3x - 2y = 4
A fraction becomes `1/3` when 2 is subtracted from the numerator and it becomes `1/2` when 1 is subtracted from the denominator. Find the fraction.
Complete the activity.
The length of the rectangle is 5 more than twice its breadth. The perimeter of a rectangle is 52 cm, then find the length of the rectangle.
The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.
The ratio of two numbers is 2:3. If 5 is added in each numbers, then the ratio becomes 5:7 find the numbers.
The ratio of two numbers is 2:3.
So, let the first number be 2x and the second number be `square`.
From the given condition,
`((2x) + square)/(square + square) = square/square`
`square (2x + square) = square (square + square)`
`square + square = square + square`
`square - square = square - square`
`- square = - square`
x = `square`
So, The first number = `2 xx square = square`
and, Second number = `3 xx square = square`
Hence, the two numbers are `square` and `square`
Read the following passage:
Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively. |
Based on the above information, answer the following questions:
- Represent the following information algebraically (in terms of x and y).
- (a) What is the prize amount for hockey?
OR
(b) Prize amount on which game is more and by how much? - What will be the total prize amount if there are 2 students each from two games?
Rehana went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Rehana got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 did she received.
