find the b numbers of solution of the following pair of linear equations : 3x - 4y = 5 ,6x - 8y - 10=0
Answers
Answer :
No. of solutions = 0
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 - 4y = 5 → 3x - 4y - 5 = 0
6x - 8y - 10 = 0
Now ,
Comparing the given linear equations with the general equations ax + bx + c = 0 and ax' + by' + c' = 0 respectively , we have ;
a = 3
a' = 6
b = -4
b' = -8
c = -5
c' = -10
Now ,
a/a' = 3/6 = 1/2
b/b' = -4/-8 = 1/2
c/c' = -5/-10 = 1/2
Clearly ,
a/a' = b/b' = c/c'
Thus ,
The given pair of lines are parallel and hence there will be no solution .