(1) Whether the following pair of L.E’s are Parallel ? Justify? 6x-4y+10=0 and 3x-2y+6=0.

Question

(1) Whether the following pair of L.E’s are
Parallel ? Justify? 6x-4y+10=0 and
3x-2y+6=0.

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Rylee 7 months 2021-10-13T17:48:02+00:00 1 Answer 0 views 0

Answers ( )

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    2021-10-13T17:49:11+00:00

    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 ;

    6x – 4y + 10 = 0 ——–(1)

    3x – 2y + 6 = 0 ——–(2)

    Clearly , we have ;

    a = 6

    a’ = 3

    b = -4

    b’ = -2

    c = 10

    c’ = 6

    Now ,

    a/a’ = 6/3 = 2

    b/b’ = -4/-2 = 2

    c/c’ = 10/6 = 5/3

    Clearly ,

    a/a’ = b/b’ ≠ c/c’ , thus the given linear equations are parallel .

    Hence justified .

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