How can you tell that a system of linear equations will have infinitely many solutions without computation?

A system of linear equations will have infinitely many solutions if the coefficients can be manipulated so that they are the same for all variables.

According to the question;

For instance; if we have equations;

The second equation can be manipulated so that it is similar to the first by dividing through by 3.

As such, the system of equations will have infinitely many solutions.

Read more:

link

If you can manipulate the two equations so that they have exactly the same coefficients (e. g., 3x + 4y = 8 and 2x + 4y = 8), then you conclude that the two lines coincide (overlap), and that there are thus infinitely many solutions.

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.