determine whether the system of alinear equqtion has one and only one solutions or no solutions find all solutions whenever they exits

Question

3x- 4y =12
6x -8y =24

Answer 1

You will notice that by multiplying the fist equation by two (2), you get exactly the second equation.

This means that the second equation is a linear transformation of the first, and geometrically means that the lines corresponding to the two equations are coincident.

Algebraically, it means that there are infinite solutions, depending on an arbitrary finite value of one of the variables.
One possible solution set is:
Let x=t (any finite real value)
then
(x,y)=(t,(3t-12)/4)