Advertisements
Advertisements
Question
Solve the following pair of linear equation by the elimination method and the substitution method.
3x – 5y – 4 = 0 and 9x = 2y + 7
Solution
3x – 5y – 4 = 0 and 9x = 2y + 7
By elimination method
3x – 5y – 4 = 0
3x – 5y = 4 ...(i)
9x = 2y + 7
9x – 2y = 7 ...(ii)
Multiplying equation (i) by 3, we get
9 x – 15 y = 11 ...(iii)
9x – 2y = 7 ...(ii)
Subtracting equation (ii) from equation (iii), we get
-13y = -5
`y = -5/13`
Putting value in equation (i), we get
3x – 5y = 4 ...(i)
`3x - 5(-5/13) = 4`
Multiplying by 13 we get
39x + 25 = 52
39x = 27
x = `27/39`
x = `9/13`
Hence, our answer is `x = 9/13 and y = - 5/13`
By substitution method
3x - 5y- 4 = 0
9x - 2y - 7 = 0
`y = (3x - 4)/5`
Putting `y = (3x - 4)/5-7 = 0`
45x - 6x + 8 - 35 = 0
39x = 27
`x = 27/39`
`x =9/13`
Putting `x = 9/13`
y = `(3xx9/13 - 4)/5`
y = `(27 - 52)/65`
y = `-25 /65`
y = `-5/13`
Hence, `x = 9/13` and `y = -5/13`
APPEARS IN
RELATED QUESTIONS
Solve the following system of linear equations by using the method of elimination by equating the coefficients √3x – √2y = √3 = ; √5x – √3y = √2
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.
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.
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 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.
2x - y = 5 ; 3x + 2y = 11
Solve the following simultaneous equation.
`x/3 + y/4 = 4; x/2 - y/4 = 1`
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.
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.
If 52x + 65y = 183 and 65x + 52y = 168, then find x + y = ?
Complete the activity.
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
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.
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`
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?
