Write the condition for which the pair of liner
equations a1x + b1y + c1 = 0,
a2x +b2y + c2= 0 said to be inconsistent.
Answers
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 .