Question

Find the value of k such that the system of equations kx + 10y = 3 9x - 15y = - 19

Answer 1

Given,

kx+10y=3 .......(1)

9x-15y=-19 .......(2)

Let two system of equations be

ax+by=c

px+qy=d

The above system of equations have no solution when

`(a)/(p)=(b)/(q)=\\e(c)/(d)`

Comapring with the given equations, we get

a=k, b=10, c=3 p=9, q=-15, d=-19.

So, the given system of equations has no solution if

`\begin{gathered} (k)/(9)=(10)/(-15)\\e(3)/(-19) \\ \end{gathered}`

`\begin{gathered} (k)/(9)=(10)/(-15) \\ k=(10)/(-15)*9 \\ k=(-2*9)/(3) \\ k=-6 \end{gathered}`

So, the value of k is -6.