Question

15) Find the equation of the line which passes
through the point of intersection of lines
x+y+9=0, 2x + 3y +1=0 and which
makes X-intercept 1.
Answer me fast ..​

Answer 1

Answer:

17x + 27y = 17

Step-by-step explanation:

To find---> Equation of line which passes through intersection of lines

x + y + 9 = 0

2 x + 3y + 1 = 0

and which makes x intercept 1 .

Solution---> Given lines equation

x + y + 9 = 0.................. (1)

2x + 3y + 1 = 0.................. (2)

Requried line goes from intersecting point of these two lines so first we find coordinates of intersecting point by solving equation(1) and (2) .

x + y + 9 = 0

=> y = -9 - x

Putting y = -9 - x in equation ( 2 ) we get

2x + 3 (-9 - x ) +1 = 0

2x - 27 - 3x + 1 = 0

- x - 26 = 0

x = -26

Putting x = -26 in y = -9 - x

y = -9 - (-26)

= -9 + 26

y= 17

Coordinates of intersecting points

= ( -26 , 17 )

Let equation of required line be

x / a + y / b = 1................. (3)

So, intercept cut by line from x axis = a

Intercept cut by line from y axis = b

ATQ , Intercept cut from x axis by line = 1

a = 1

Putting a = 1 in equation (3)

x / 1 + y / b = 1

multiplying whole equation by b

b x + b ( y / b ) = b × 1

b x + y = b .................... (4)

Now line (4) passes through intersecting point of line (1) and line (2) so satisfying equation (4) by (-26 , 17 ) we get

b ( - 26 ) + 17 = b

=> - 26 b + 17 = b

=> - 26 b - b = -17

=> - 27 b = -17

=> b = 17 / 27

Putting b = 17 / 27 in equation ( 4 ) we get required equation of line

(17 / 27 ) x + y = 17 / 27

multiplying equation by 27

27 ( 17 / 27 ) x + 27 y = 27 ( 17 / 27 )

=> 17 x + 27 y = 17