Question

9. Find the equation of the straight line parallel to the line 3x + 4y=7 and passing through the point
of intersection of the lines x - 2y - 3 = 0 and x + 3y - 6=0.​

Answer 1

Answer:

3x + 4y - 15 = 0

Step-by-step explanation:

Solving x - 2y - 3 = 0  and x + 3y - 6 = 0

⇒ x - 2y - 3 - (x + 3y - 6) = 0 -0

⇒ - 5y + 3 = 0     ⇒ y = 3/5

 Thus, x - 2(3/5) - 3 = 0

⇒ x = 6/5 + 3 = 21/5

     Hence the line passes through (21/5 , 3/5).

As it is parallel to 3x + 4y = 7, their slope should be same.

Slope is given by m in y = mx + c.

  Here,  3x + 4y = 7  

       ⇒ y = (-3/4)x + (7/4).

Slope of that is - 3/4. And  a point on it is (21/5 , 3/5).

Equation:

  ⇒ (y - 3/5) = (-3/4) (x - 21/5)

  ⇒ 4(5y - 3)/5 = -3(5x - 21)/5

  ⇒ 20y - 12 = - 15x + 63

  ⇒ 15x + 20y - 75 = 0

  ⇒ 3x + 4y - 15 = 0