Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72 - Mathematics

Advertisements
Advertisements
Sum

Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72

Advertisements

Solution

The given system of equation is

15x + 4y = 61 ….(1)

4x + 15y = 72 ….(2)

Let us eliminate y.

The coefficients of y are 4 and 15.

The L.C.M. of 4 and 15 is 60. So, we make the coefficients of y as 60.

Multiplying (1) by 15 and (2) by 4, we get

225x + 60y = 915 ….(3)

16x + 60y = 288 ….(4)

Substracting (4) from (3), we get

209x = 627 ⇒ x = 3

Putting x = 3 in (1), we get

15 × 3 + 4y = 61 45 + 4y = 61

4y = 61 – 45 = 16 ⇒ y = 4

Hence, the solution is x = 3, y = 4.

Verification: On putting x = 3 and y = 4 in the given equations, they are satisfied. Hence, the solution is correct.

  Is there an error in this question or solution?

RELATED QUESTIONS

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 pair of linear equations by the elimination method and the substitution method.

`x/2 + (2y)/3 = -1 and x - y /3 = 3`


Form the pair of linear equations in the following problems, and find their solutions (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 equations in the following problems, and find their solutions (if they exist) by the elimination method:

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.


Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.


 

Form the pair of linear equations in the following problems, and find their solutions (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.


Two types of boxes A, B are to be placed in a truck having a capacity of 10 tons. When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons. But when 260 boxes of type A are loaded in the truck, it can still accommodate 40 boxes of type B, so that it is fully loaded. Find the weight of each type of box.


Out of 1900 km, Vishal travelled some distance by bus and some by aeroplane. The bus travels with an average speed of 60 km/hr and the average speed of the aeroplane is 700 km/hr. It takes 5 hours to complete the journey. Find the distance, Vishal travelled by bus.

 

The denominator of a fraction is 1 less than twice its numerator. If 1 is added to numerator and denominator respectively, the ratio of numerator to denominator is 3 : 5. Find the fraction.


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.


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.


In  ΔABC, the measure of angle A is equal to the sum of the measures of ∠B and ∠C. Also the ratio of measures of ∠B and ∠C is 4 : 5. Then find the measures of angles of the triangle.


In a competitive examination, there were 60 questions. The correct answer would carry 2 marks, and for incorrect answer 1 mark would be subtracted. Yashwant had attempted all the questions and he got total 90 marks. Then how many questions he got wrong?


Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay's age?


A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to this  number, the sum is equal to the number obtained by interchanging the digits. Find the  number.


The total cost of 8 books and 5 pens is 420 rupees and the total cost of 5 books and 8 pens is 321 rupees. Find the cost of 1 book and 2 pens.


The ratio of incomes of two persons is 9 : 7. The ratio of their expenses is 4 : 3. Every person saves rupees 200, find the income of each.


If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 9 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.


Solve the following simultaneous equation.

x + y = 11 ; 2x - 3y = 7 


Solve the following simultaneous equation.

2x + y = -2 ; 3x - y = 7 


Solve the following simultaneous equation.

2x - y = 5 ; 3x + 2y = 11 


Solve the following simultaneous equation.

`x/3 + y/4 = 4; x/2 - y/4 = 1`


Solve the following simultaneous equation.

`x/3 + 5y = 13 ; 2x + y/2 = 19`


The difference between an angle and its complement is 10° find measure of the larger angle.


If 52x + 65y = 183 and 65x + 52y = 168, then find x + y = ?



Complete the following table to draw the graph of 3x − 2y = 18

x 0 4 2 −1
y − 9 ______ ______ ______
(x, y) (0, −9) (______, _______) (______, _______) ______

The sum of the two-digit number and the number obtained by interchanging the digits is 132. The digit in the ten’s place is 2 more than the digit in the unit’s place. Complete the activity to find the original number.

Activity: Let the digit in the unit’s place be y and the digit in the ten’s place be x.

∴ The number = 10x + y

∴ The number obtained by interchanging the digits = `square`

∴ The sum of the number and the number obtained by interchanging the digits = 132

∴ 10x + y + 10y + x = `square`

∴ x + y = `square`      .....(i)

By second condition,

Digit in the ten’s place = digit in the unit’s place + 2

∴ x – y = 2     ......(ii)

Solving equations (i) and (ii)

∴ x = `square`, y = `square`

Ans: The original number = `square`


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


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 solution of the equation ax + by + 5 = 0 and bx − ay − 12 = 0 is (2, – 3). Find the values of a and b


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


Evaluate: (1004)3


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`


A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.


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.


Share
Notifications



      Forgot password?
Use app×