How do you determine whether a linear system has one solution, many solutions, or no solution when given y=-x+6 and y=3/4x-1?

1 Answer
Mar 10, 2018

Given, y=-x+6

or, x+y=6.....................1

and, y=3/4 x-1

or, 3x-4y=4....................................2

Now,we know for two equations , ax +by=c and px +qy=k

if, a/p ne b/q then they will have unique solution.

if, a/p=b/q ne c/k then they will have no solution.

if, a/p=b/q=c/k then they will have multiple solutions.

here in this case we get, 1/3 ne -(1/4) i.e a/p ne b/q,so it will have one solution only.