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 pair of linear equation by the elimination method and the substitution method.
3x – 5y – 4 = 0 and 9x = 2y + 7
Form the pair of linear equation in the following problem, and find its solution (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.
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.
The sum of a two-digit number and the number formed by reversing the order of digit is 66. If the two digits differ by 2, find the number. How many such numbers are there?
In an envelope there are some 5 rupee notes and some 10 rupee notes. Total amount of these notes together is 350 rupees. Number of 5 rupee notes are less by 10 than twice number of 10 rupee notes. Then find the number of 5 rupee and 10 rupee notes.
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 = 5 ; 3x + 2y = 11
Solve the following simultaneous equation.
`x/3 + 5y = 13 ; 2x + y/2 = 19`
Solve the following simultaneous equation.
`2/x + 3/y = 13` ; `5/x - 4/y = -2`
By equating coefficients of variables, solve the following equation.
5x + 7y = 17 ; 3x - 2y = 4
By equating coefficients of variables, solve the following equation.
4x + y = 34 ; x + 4y = 16
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 solution of the equation ax + by + 5 = 0 and bx – ay – 12 = 0 is (2, – 3). Find the values of a and b.
Evaluate: (1004)3
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.
