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

Question

Mathematics

Charlie Simmons

19 May, 19:14

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

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Malik Rollins · Answer 1

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.