Question

samikaran Pranali De jode x-4y-6=0 and 3x-12y-18=0 da De kitne HAL Honge​

Answer 1

Answer :

No solution

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 equations are ;

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

3x - 12y - 18 = 0 ---------(2)

Now ,

Comparing eq-(1) and eq-(2) with ax + by + c = 0 and a'x + b'y + c' = 0 respectively , we have ;

a = 1

b = -4

c = -6

a' = 3

b' = -12

c' = -18

Now ,

a/a' = 1/3

b/b' = -4/-12 = 1/3

c/c' = -6/-18 = 1/3

Clearly ,

a/a' = b/b' = c/c'

Thus ,

The given lines are parallel , ie. they are non-intersecting lines and hence there will be no solution of the given system of linear equations .