Question

For what value of k system of equations 3x + 4y = 19, y – x = 3 and 2x + 3y = k has a solution?​

Answer 1

Answer:

Consider the given equations.

4x+ky+8=0    ……. (1)

2x+3y+7=0    …… (2)

 

The general equations,

a  

1

​  

x+b  

1

​  

y+c  

1

​  

=0

a  

2

​  

x+b  

2

​  

y+c  

2

​  

=0

 

Therefore,

a  

1

​  

=4,b  

1

​  

=k,c  

1

​  

=8

a  

2

​  

=2,b  

2

​  

=3,c  

2

​  

=7

 

Since, the condition of unique solution is

a  

2

​  

 

a  

1

​  

 

​  

 



=  

b  

2

​  

 

b  

1

​  

 

​  

 

 

Therefore,

2

4

​  

 



=  

3

k

​  

 

3

k

​  

 



=2

k



=6

 

Hence, k is any real number except 6.