Question

Find an equation of the line passing through the point (2, -1) and the point of intersection of the lines x + 2y = 3 and 2x - 3y = 13.

Answer 1

y=-1 is the equation of the line

Explanation:

x + 2y = 3 and

solve for x and y to get intersection point

multiply first equation by -2

`-2x -4y = -6`

`2x - 3y = 13`

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`-7y=7`

y=-1

`x + 2y = 3`

`x + 2(-1)= 3`

`x -2= 3`

x=5

intersection point is (5,-1)

(2, -1) and (5,-1)

`slope = (y_2-y_1)/(x_2-x_1) =(-1+1)/(5-2) =0`

Slope = 0 (horizontal line)

So equation becomes y =y1 value

y=-1 is the equation of the line