Question

For what value of k y - x = 6 and 3 k x + 2 y = 7 have a unique solution

Answer 1

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.

Answer 2

Step-by-step explanation:

Cells are the basic building blocks of all living things. The human body is composed of trillions of cells