Find the value of m for which the simultaneous equations and have:
a) an infinite number of solutions
b) no solutions.
mostly having trouble with a), please explain how you got your answer,
thanks
Hello,
you know that a linear equation has a straight line as it's graph.
If you have the 2 linear equations
then you know that there are infinite many common points if
and
There is no solution (or there aren't any common points) if
With your problem:
1. Rearrange your equations ( , )
2. Use the general equations which I mentioned above
3. For confirmation only: Infinite many solutions with m = -5 and no solution with m = 3.
The determinant of the coefficients is:
To have non-unique solution the determinant needs to be zero:
.
Now check which one gives infinite solutions and which one gives no solutions.*
*)Or you can use determinants again, but there is no point. Because you just need to check two values.