Math, asked by KrithickG2100, 7 months ago

For what value of K does the pair of equations given below has a unique solution y-x=0, 3kx+2y=7

Answers

Answered by AlluringNightingale
14

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

Hence ,

k can be any real number other than -2/3 .

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