Question

Find the equation of the line passing through the point of
intersection of 2x+y=5 and x + 3y+8 = 0 and parallel to the line 3x + 4y=7​

Answer 1

Answer:

3 x + 4 y + 3 = 0

Step-by-step explanation:

Given :

Equation of lines :

2 x + y = 5

2 x = 5 - y  ... ( i )

x + 3 y + 8 = 0 ... ( ii )

Solving for x and y to get intersection point :

Multiply by 2 in ( ii )

2 x = - 16 - 6 y .... ( iii )

From ( i )  and  ( ii )

5 - y = - 16 - 6 y

5 y = - 21

y = - 21 / 5

Putting 2 x + y = 5  to get value of x :

2 x = 5 + 21 / 5

x = 23 / 5

Now we have passing point ( 23 / 5 , - 21 / 5 ) .

Also given parallel line :

3 x + 4 y = 7

= > 3 x + 4 y - 7 = 0

Slope of line = - A / B

= > - 3 / 4

We know if when lines are parallel their slope always equals

= > m' = - 3 / 4

Now equation of line :

y + 21 / 5 = - 3 / 4 ( x - 23 / 5 )

= >  3 x + 4 y + 3 = 0

Therefore , we get required answer.