Question

For what value of K will the system of equations given below have no solution?


2x + 5y = 9
-3x - K y = 4

Answer 1

K = 15/2 = 7.5

Answer 2

given two linear equations in two variables

a1x + b1y + c1 = 0 and
a2x + b2y + c2 = 0

they will not have a solution if

a1 b1 c1
---- = ---- ╪ ----
a2 b2 c2

Rearranging given equations we get
2x + 5y - 9 = 0
-3x - Ky - 4 = 0

Here obviously a1/a2 ╪ c1/c2 because 2/-3 ╪ -9/-4
so if give value to K such that b1/b2 = a1/a2, then there will be no solution

b1 2
so ---- has to be made = -----
b2 -3

5 2
so ----- = -----
-k -3
cross multiplying
-15 = -2k
-15/-2 = k

so k = 15/2

It looks like a long calculation, but once you know what is to be done, you can do it orally and very quickly.......