Question

Write the condition for which the pair of liner

equations a1x + b1y + c1 = 0,
a2x +b2y + c2= 0 said to be inconsistent.
​

Answer 1

Answer:

a1/a2 = b1/b2 ≠ c1/c2

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 ;

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

The given lines is said to be inconsistent if they are parallel .

Thus,

If a1/a2 = b1/b2 ≠ c1/c2 , then the lines will be parallel and hence they will be inconsistent .