Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method

Solve the following pair of linear equations by the elimination method and the substitution method:

x + y = 5 and 2x – 3y = 4

Solve the following system of linear equations :

2(ax – by) + (a + 4b) = 0

2(bx + ay) + (b – 4a) = 0

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 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 :

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.

Solve the following system of linear equations by using the method of elimination by equating the coefficients √3x – √2y = √3 = ; √5x – √3y = √2

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 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: 

3x + 4y = 10 and 2x – 2y = 2

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

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.

Solve (a – b) x + (a + b) y = `a^2 – 2ab – b^2 (a + b) (x + y) = a^2 + b^2`

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?

Solve for x and y : `\frac { ax }{ b } – \frac { by }{ a } = a + b ; ax – by = 2ab`

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

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

Solve the following pair of linear equations by the elimination method and the substitution method

3x – 5y – 4 = 0 and 9x = 2y + 7