Question

3 X + 2 y equal 5 2 X + k y = 7 are in constant find the value of k

Answer 1

If a pair of linear  equations is given by

a  

1

​  

x+b  

1

​  

y+c  

1

​  

=0 and  

a  

2

​  

x+b  

2

​  

y+c  

2

​  

=0  

When the system of linear equations will represent two Parallel Lines there is no point of intersection and consequently, there is no pair of values of x and y which satisfy both equations. Thus, the system has no solution and such pair of linear equation is inconsistent pair of linear equations

For parallel lines(inconsistent)

a  

2

​  

 

a  

1

​  

 

​  

=  

b  

2

​  

 

b  

1

​  

 

​  

 



​  

=  

c  

2

​  

 

c  

1

​  

 

​  

 

The given pair of linear equations are  

5x+ky+7=0          ........(1)

x+2y−3=0           .........(2)

On comparing with General form of a pair of linear equations  in two variables x & y is:  

we get

a₁=5, b₁=k, c₁=7, a₂=1, b₂=2, c₂=-3

5/1=k/2≠7/-3

k/2=5

∴k=10

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