From the point where the lines 3x + 2y = 8 and x - y = 9 meet perpendicular line is drawn to the x and y axes. What is their equation

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equations of the lines perpendicular to the x and y axes from the point of intersection of 3x + 2y = 8 and x - y = 9 has to be determined.

First to determine the point of intersection, the equations have to be solved for x and y.

3x + 2y = 8 ...(1)

x - y = 9 ...(2)

(2) gives x = 9 + y

Substitute this in (1)

=> 3(9 + y) + 2y = 8

=> 27 + 5y = 8

=> y = -3.8

x = 5.2

The equation of the line from this point perpendicular to the x-axis has a slope equal to inf.

`(y + 3.8)/(x - 5.2) = 1/0`

=> x = 5.2

The equation of the line from this point perpendicular to the y-axis has a slope equal to 0.

` (y + 3.8)/(x - 5.2) = 0`

=> y + 3.8 = 0

The required line perpendicular to the x-axis is x - 5.2 = 0 and the line perpendicular to the y axis is y + 3.8 = 0

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