For what value of K does the pair of equations given below has a unique solution y-x=0, 3kx+2y=7
Answers
Answer :
k ≠ -2/3
(k can be any real no. other than -2/3)
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 are ;
y - x = 0
3kx + 2y = 7
The given linear equations can be rewritten in their general forms as ;
-x + y + 0 = 0
3kx + 2y - 7 = 0
Clearly , we have ;
a = -1
a' = 3k
b = 1
b' = 2
c = 0
c' = -7
For the given pair of linear equations to have a unique solution , a/a' ≠ b/b' .
Thus ,
=> -1/3k ≠ 1/2
=> -1 × 2 ≠ 3k
=> 3k ≠ -2
=> k ≠ -2/3