Advertisements
Advertisements
प्रश्न
By equating coefficients of variables, solve the following equation.
4x + y = 34 ; x + 4y = 16
Advertisements
उत्तर
4x + y = 34 ...(I)
x + 4y = 16 ...(II)
Adding (I) and (II) we get,
4x + y = 34
x + 4y = 16
5x + 5y = 50
⇒ x + y = 10 ...(III)
Subtracting (II) from (I) we get,
4x + y = 34
x + 4y = 16
- - -
3x - 3y = 18
⇒ x - y = 6 ...(IV)
Adding (III) and (IV) we get,
x + y = 10
x - y = 6
2x = 16
⇒ x = 8
Putting the value of x in (I) we get,
∴ 4x + y = 34
⇒ 4 (8) + y = 34
⇒ y = 34 - 32
⇒ y = 2
Thus, x = 8, y = 2
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 – √2y = √3 = ; √5x – √3y = √2
Solve the following pair of linear equation by the elimination method and the substitution method:
x + y = 5 and 2x – 3y = 4
Solve the following pair of linear equation by the elimination method and the substitution method:
3x + 4y = 10 and 2x – 2y = 2
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.
The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.
Solve the following simultaneous equation.
x - 2y = -1 ; 2x - y = 7
Solve the following simultaneous equation.
x − 2y = −2 ; x + 2y = 10
By equating coefficients of variables, solve the following equations.
3x - 4y = 7; 5x + 2y = 3
By equating coefficients of variables, solve the following equation.
x − 2y = −10 ; 3x − 5y = −12
If 52x + 65y = 183 and 65x + 52y = 168, then find x + y = ?
Difference between two numbers is 3. The sum of three times the bigger number and two times the smaller number is 19. Then find the numbers
Solve: 99x + 101y = 499, 101x + 99y = 501
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 semi perimeter of a rectangular shape garden is 36 m. The length of the garden is 4 m more than its breadth. Find the length and the breadth of the garden
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ______.
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`
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.
