Heyo everyone,
So I was doing some practise questions for methods and I was struggling a little on this one.. could someone please help me out?
Q. Find the value of m for which the following simultaneous equations have a unique solution:
-4x + my = -5
-3mx + y =0
I figured out the determinant to be 3m^2 - 4 when I put the coefficients into a matrix and equated it to zero to find the values of m for which they have no unique solutions…
But I’m a little stumped by what ‘a unique solution means’…
Is there another approach I’m supposed to be using?
Thank you!
(Firstly, sorry if this is really wrong I have no confidence in my maths ability.)A unique solution means that those two lines have one point of intersection, so are orientated somehow like an X (as opposed to parallel with no solutions or on top of each other with infinite solutions).
I don't know how to do it the matrix way, but the way I would do the question would be to:
1. substitute the two equations into eachother like you would to find the point of intersection.
2. then when you get the quadratic with m in it you want to find the discriminant (Δ=b
2-4ac)
3. for one solution discriminant=0, so let Δ=0, then solve for m, and the value you get for m should be the value of m when the lines have one unique solution
my (hopefully correct) working out
(If you prefer using matrices you don't have to do it this way)
Also, I cannot view your photo from your second post