System of Equations with Zero Solution

Good morning,

Is the opposite also true with this rule? The rule in the image attached is for systems of equations with no solution. It says if the coefficients are the same but the constants are different, no solution can be found.

Is it also true that if the constants are the same but the coefficients are different, that no solution can be found?

No, it depends.

  1. 4x + 2y = 7 and 2x + y = 7 → No solutions

  2. 5x + 2y = 7 and 3x + y = 7 → Unique solution

  3. 4x + 10y = 0 and 2x + 5y = 0 → Infinite solutions

Got it, so the consistent rule is

equal coefficients and different constants = no solutions

but different coefficients and equal constants = none, infinite or unique solutions, depending on the case

thank you!