For what value of k, do the equations 2x – 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines
Answers
Answer :
k = -9/2
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 ;
2x - 3y + 10 = 0 --------(1)
3x + ky + 15 = 0 --------(2)
Clearly , we have ;
a = 2
a' = 3
b = -3
b' = k
c = 10
c' = 15
Now ,
For the given lines to be coincident ,
a/a' = b/b' = c/c'
Thus ,
=> 2/3 = -3/k = 10/15
=> 2/3 = -3/k = 2/3
=> 2/3 = -3/k
=> k = -3 × 3/2
=> k = -9/2
Hence , k = -9/2 .
Answer:
same as the above text
Step-by-step explanation:
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