on comparing the ratios A1/a2 b1/b2 and C1/C2 1)3x-5y=11 & 6x-10y=7
Answers
Answér :
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 linear equations are ;
3x - 5y = 11
6x - 10y = 7
The given equations can be rewritten as ;
3x - 5y - 11 = 0
6x - 10y - 7 = 0
Clearly , we have ;
a1 = 3
a2 = 6
b1 = -5
b2 = -10
c1 = -11
c2 = -7
Now ,
a1/a2 = 3/6 = 1/2
b1/b2 = -5/-10 = 1/2
c1/c2 = -11/-7 = 11/7
Clearly ,
a1/a2 = b1/b2 ≠ c1/c2
Thus ,
The given equations has no solution .