Question

For what value of k system of equations: x + 2y = 3 and 5x + ky + 7 = 0 has a unique solution.

Answer 1

Given pair of Linear Equations are:
x +2y = 3
5x + ky +7= 0

The Given equations can be written rewritten as :
x +2y - 3 = 0
5x + ky +7= 0

On Comparing the Given eqs with standard form
a1x + b1y + c1 = 0 & a2x + b2y + c2= 0

Here, a1= 1, b1= 2 , c1= -3 &
a2= 5 , b2= k , c2= 7

A pair of linear equation has unique solution if ,
a1/a2 ≠ b1/b2
⅕ ≠ 2/k
k ≠ 10

So, the lines have unique solution for all real values of k except 10.

HOPE THIS WILL HELP YOU...

Answer 2

Heya Friend ,
Here is your answer !!

The two given equations are :
x + 2y = 3
=> x + 2y - 3 = 0 ...... ( i )

and

5x + ky + 7 = 0 ..... ( ii )

For two equations to have a unique solution ,
a1 / a2 != b1 / b2

so ,

ATQ ,

1 / 5 != 2 / k
=> k != 10 .

Hence , for the two equations to have only one solution , k can have any value except 10 . [ Answer ]

Hope it helps you !!