Question

2. The following is a pair of linear equations kx – y = 2 and 6x – 2y = 3 Answer the questions with reference to the given pair of equations (2 Marks) i. Write down the condition for unique solution ii. Find the value of K 3. Find the solution of any one of the following (3 Marks) i. x + 2y = -1 and 2x -3y =12 (Substitution method) ii. 2x + 3y = 7 and 3x + 4y = 10 (Elimination method) 4. Solve the following pair of equations graphically (4 Marks) 2x + y = 6 and 2x – y + 2 = 0 Plot at least 3 points for each equation 2x + y = 6 2x – y + 2 = 0 X Y X Y

Answer 1

Step-by-step explanation:

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Answer 2

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Given system of equations are

6x - 2y = 3

6x - 2y - 3 = 0 ----( 1 )

kx - y = 2

kx - y - 2 = 0 ----( 2 )

Compare above equations with

a1 x + b1 y + c1 = 0 and

a2 x + b2 y + c2 = 0 , we get

a1 = 6 , b1 = -2 , c1 = -3 ;

a2 = k , b2 = -1 , c2 = -2 ;

Now ,

a1/a2 ≠ b1/b2

[ Given they have Unique solution ]

6/k ≠ ( -2 )/( -1 )

6/k ≠ 2

k/6 ≠ 1/2

k ≠ 6/2

k ≠ 3

Therefore ,

For all real values of k , except k≠ 3,

Above equations has unique solution.

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