Advertisements
Advertisements
Question
Solve the following pair of linear equation by the elimination method and the substitution method:
x + y = 5 and 2x – 3y = 4
Solution
x + y = 5 and 2x – 3y = 4
By elimination method
x + y = 5 ...(i)
2x – 3y = 4 ...(ii)
Multiplying equation (i) by (ii), we get
2x + 2y = 10 ...(iii)
2x – 3y = 4 ...(ii)
Subtracting equation (ii) from equation (iii), we get
5y = 6
y = `6/5`
Putting the value in equation (i), we get
`x = 5 - (6/5) = 19/5`
Hence, `x = 19/5 and y = 6/5`
By substitution method
x + y = 5 ...(i)
Subtracting y both side, we get
x = 5 - y ...(iv)
Putting the value of x in equation (ii) we get
2(5 – y) – 3y = 4
-5y = -6
`y = (-6)/-5`
`y = 6/5`
Putting the value of y in equation (iv) we get
`x = 5 – 6/5`
`x = 19/5`
Hence, `x = 19/5` and `y = 6/5`.
APPEARS IN
RELATED QUESTIONS
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:
3x + 4y = 10 and 2x – 2y = 2
Solve the following pair of linear equation by the elimination method and the substitution method.
`x/2 + (2y)/3 = -1 and x - y /3 = 3`
Form the pair of linear equation in the following problem, and find its solution (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?
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.
Solve the following simultaneous equation.
2x + y = -2 ; 3x - y = 7
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`
If 52x + 65y = 183 and 65x + 52y = 168, then find x + y = ?
Complete the activity.
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 angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.
The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.
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.
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.
