Question

(1) Whether the following pair of L.E's are
Parallel ? Justify? 6x-4y+10=0 and
3x-2y+6=0.

Answer 1

Note:

★ A linear equation is two variables represent a straight line .

★ The word consistent is used for the system of equations which consists any solution .

★ The word inconsistent is used for the system of equations which doesn't consists any solution .

★ Solution of a system of equations : It refers to the possibile values of the variable which satisfy all the equations in the given system .

★ A pair of linear equations are said to be consistent if their graph ( Straight line ) either intersect or coincide each other .

★ A pair of linear equations are said to be inconsistent if their graph ( Straight line ) are parallel .

★ If we consider equations of two straight line

ax + by + c = 0 and a'x + b'y + c' = 0 , then ;

• The lines are intersecting if a/a' ≠ b/b' .

→ In this case , unique solution is found .

• The lines are coincident if a/a' = b/b' = c/c' .

→ In this case , infinitely many solutions are found .

• The lines are parallel if a/a' = b/b' ≠ c/c' .

→ In this case , no solution is found .

Solution :

Here ,

The given linear equations are ;

6x - 4y + 10 = 0 --------(1)

3x - 2y + 6 = 0 --------(2)

Clearly , we have ;

a = 6

a' = 3

b = -4

b' = -2

c = 10

c' = 6

Now ,

a/a' = 6/3 = 2

b/b' = -4/-2 = 2

c/c' = 10/6 = 5/3

Clearly ,

a/a' = b/b' ≠ c/c' , thus the given linear equations are parallel .

Hence justified .