Advertisements
Advertisements
Question
By equating coefficients of variables, solve the following equation.
5x + 7y = 17 ; 3x - 2y = 4
Advertisements
Solution
5x + 7y = 17 ...(I)
3x - 2y = 4 ...(II)
Multiply (I) with 3 and (II) with 5
15x + 21y = 51 ...(III)
15x - 10y = 20 ...(IV)
Subtracting (IV) from (III) we get,
15x + 21y = 51
15x - 10y = 20
- + -
31y = 31
⇒ y = 1
Putting this value of y in (I) we get
∴ 5x + 7y = 17
5x + 7 × 1 = 17
⇒ 5x = 10
⇒ x = 2
Thus, x = 2, y = 1
APPEARS IN
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 (a – b) x + (a + b) y = `a^2 – 2ab – b^2 (a + b) (x + y) = a^2 + b^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 solutions (if they exist) by the elimination method:
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
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.
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.
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.
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.
`x/3 + y/4 = 4; x/2 - y/4 = 1`
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
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`
Solve: 99x + 101y = 499; 101x + 99y = 501
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?
