How do you know when an equation has infenitely any solutions? How do you know when there is no solution?

Question

This is just one concept I am not understanding...can anyone help?

Answer 1

Essentially, there might be an equation whose left side is a sum of the earlier equations provided, but then the right side might vary...

example .. . .

Ax + By = C

kA x + kBy = D

if D is not kC then the system yields no solution

if D is kC, the system yields infinite solution.

if you have a GD calculator, then you might want to employ its RREF on a matrix.

if your RREF on the matrix has a row where the last row is almost zero except for the last entry, then it is the case of no solution

if the RREF has a zero row, the system has infinite solution. (This has to be noted that the coefficient matrix is square.)