Thread: linear solutions

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

Originally Posted by DivideBy0

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.

Thanks

Originally Posted by DivideBy0

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

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.