Question: Find the single equation represented by the following pair of straight lines: x - y = 2 and 2x - 3y = 5.

Solution:
Given,

Equation of line i is x - y = 2
or, x - y - 2 = 0

Equation of line ii is 2x - 3y = 5
or, 2x - 3y - 5 = 0

Now,

Multiplying the equations of line i and ii, we get,

(x - y -2)(2x - 3y - 5) = 0

or, x(2x - 3y -5) - y(2x -3y -5) -2(2x -3y -5) = 0

or, 2x² - 3xy -5x -2xy +3y² +5y -4x +6y +10 = 0

or, 2x² -3xy -2xy -5x -4x +5y +6y +3y² +10 = 0

or, 2x² -5xy -9x +11y +3y² +10 = 0

Hence, 2x² +3y² -5xy -9x +11y +10 = 0 is the required single equation of the line represented by the above two lines.


Related Notes and Solutions:

Here is the website link to all the important formulae of Coordinate Geometry of Class 10.

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