Question

Two lines are given to be parallel the equation of one of the lines is 4 + 3 = 5, then one of the possible second parallel line is​

Answer 1

Step-by-step explanation:

Equation of a line ax + by + c = 0 parallel to given line is ax + by + k = 0 here k is any real number. Therefore , Required parallel line is 4x + 3y = k Example : 4x + 3y = 5 , 4x + 3y = - 7Read more on Sarthaks.com - https://www.sarthaks.com/838092/lines-given-parallel-the-equation-one-the-equation-then-find-the-equation-the-second-line

Answer 2

Given : two lines are given to be parallel the equation of one of the lines is 4x + 3y = 5,  one of the possible second parallel line  

To Find : one of the possible second parallel line

Solution:

Pair of linear equations

a₁x  +  b₁y + c₁  =  0

a₂x  +  b₂y + c₂  =  0

Consistent

if a₁/a₂ ≠ b₁/b₂   (unique solution  and lines intersects each others)

  a₁/a₂ = b₁/b₂ = c₁/c₂   (infinite solutions and line coincide each other )

Inconsistent

if  a₁/a₂ = b₁/b₂ ≠  c₁/c₂  ( No solution , lines are parallel to each other)

two lines are given to be parallel

Hence a₁/a₂ = b₁/b₂ ≠  c₁/c₂

4x + 3y = 5

=> parallel line can be

k₁ (4x + 3y )  = 5k₂  where k₁  ≠ k₂    and  k₁  , k₂ are non zero real numbers

For example

4x + 3y = 6

4x + 3y =  7

8x + 6y  = 5

8x + 6y  = 6

These all can be possible second parallel line

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