3 Find the ratis of and
Consistent or inconsistent . 2x + 3y =5 and 4x+6y=7
Answers
Answer :
Inconsistent
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 of lines are :
2x + 3y = 5
4x + 6x = 7
The given lines can be rewritten as ;
2x + 3y - 5 = 0
4x + 6y - 7 = 0
Clearly , we have ;
a = 2
a' = 4
b = 3
b' = 6
c = -5
c' = -7
Now ,
a/a' = 2/4 = 1/2
b/b' = 3/6 = 1/2
c/c' = -5/-7 = 5/7
Clearly ,
a/a' = b/b' ≠ c/c'
Thus ,
The given lines are parallel and hence the system is inconsistent .
Answer:
A1=2
A2=4
B1=3
B2=6
C1=-5
C2=-7
By formula
A1/A2=2/4=1/2
B1/B2=3/6=1/2
C1/C2=-5/-7=5/7
A1/A2=B1/B2 is not equal to C1/C2
Therefore it has no solution
it is inconsistent