Question

13. Find the equation of the straight line joining the point of intersection of the lines 3x- y+ 9 = 0 and x +2y= 4 and the point of intersection of the lines 2x+ y- 4 = 0 and x- 2y+3 = 0.

Answer 1

Hi ,

i ) Let P( x1 ,y1 ) is the intersecting point

of lines

3x - y + 9 = 0----( 1 )

x + 2y = 4

x = -2y + 4 -----( 2 )

put x = -2y + 4 in equation ( 1 ) , we get

3( -2y + 4 ) - y + 9 = 0

-6y + 12 - y + 9 = 0

-7y + 21 = 0

-7y = -21

y = -21/( -7 )

y = 3

put y = 3 in equation ( 2 ) , we get

x = - 2 × 3 + 4

x = -6 + 4 = -2

P( x1 , y1 ) = ( -2 , 1 )

ii ) Let Q( x2 , y2 ) is the intersecting point

of the lines

2x + y - 4 = 0 ---( 3 )

x - 2y + 3 = 0

x = 2y - 3 -----( 4 )

Put x = 2y - 3 in equation ( 3 ) we get,

2(2y - 3 ) + y - 4 = 0

4y - 6 + y - 4 = 0

5y = 10

y = 10/5 = 2

put y = 2 in equation ( 4 )

we get

x = 1

Q( x2 , y2 ) = ( 1 , 2 )

iii ) Equation of the line

joining P( x1 , y1 ) = ( -2,3)

and Q( x2 , y2 ) = ( 1 , 2 )is

(y-y1)(x2 - x1) = (x - x1)(y2-y1)

(y-3)(1+2) = (x +2)( 2 - 3 )

3y - 9 = -x - 2

x + 3y - 7 = 0

I hope this helps you.

: )