Question

Find the missing value in each of the following: 1. Write the value of k for which the system of equations x + y -4 =0 and 2x + ky -3 = 0 has no solution. 2. Find k for which the system of equations 2x – y = 5 and 6x + ky = 15 has infinitely many solutions. 3. Write the set of values of a and b for which the following system of equations has infinitely many solutions. 2x + 3y = 7 2ax + (a + b) y = 28 4. For what value of k, the following pair of linear equations has a unique solution. x + ky = 0 , 2x – y = 0 5. For what value of k, the following pair of linear equations has infinitely many solutions 10 x + 5 y – (k – 5) = 0 20 x + 10 y – k = 0

Answer 1

Answer:

Step-by-step explanation:

2x−ky+3=0

3x+2y−1=0

These equations are of the form

a  

1

​

x+b  

1

​

y+c  

1

​

=0,a  

2

​

x+b  

2

​

y+c  

2

​

=0

where a  

1

​

=2,b  

1

​

=−k,c  

1

​

=3, and a  

2

​

=3,b  

2

​

=2,c  

2

​

=−1

Now, for the given pair to have no solution,

a  

2

​

 

a  

1

​

 

​

=  

b  

2

​

 

b  

1

​

 

​

 



=  

c  

2

​

 

c  

1

​

 

​

 

3

2

​

=  

2

−k

​

 



=  

−1

3

​

 

3

2

​

=−  

2

k

​

 and  

2

−k

​

 



=  

−1

3

​

 

k=−  

3

4

​

 and k



=6

Therefore, k=−  

3

4

​