Question

Find the value of k for which the system of linear equations x+2y = 3, 5x +ky+7 = 0 is inconsistent.

pls solve it ​

Answer 1

Answer: Any system of linear equations of the form

a1x+b1y=c1  

a2x+b2y=c1  

has a unique solution only if the determinant

∣∣∣a1a2b1b2∣∣∣≠  0  

i.e.  a1b2≠  a2b1  

So, in order for the given system of equations

x+2y=3  

5x+ky=3  

to have a unique solution,

∣∣∣152k∣∣∣≠0  

i.e.  k≠10  

In other words, the given system of equations has a unique solutions for any value of  k  other than  k=10 .

Why is there a problem when  k=10 ?

If  k=10 , then the second equation becomes

5x+10y=3  

i.e.  x+2y=35  

But the first equation is

x+2y=3  

So we would have no solution to the system of equations if  k=10