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

Solve the following simultaneous equation.

2x - y = 5 ; 3x + 2y = 11 

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`

By equating coefficients of variables, solve the following equations.

3x - 4y = 7; 5x + 2y = 3

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.

If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 9 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.

Solve the following simultaneous equation.

`2/x + 3/y = 13` ; `5/x - 4/y = -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`

Solve the following simultaneous equation.

`x/3 + 5y = 13 ; 2x + y/2 = 19`