How do you know if a system or equations has one solution, no solution, or infinitely many solutions

Step-by-step explanation:

We transform the system of equations to the form:

Where a & b and d & e are relatively prime number.

If a ≠ d or b ≠ e then the system of equations has one solution.

Example:

Add both sides of equations:

    divide both sides by 5

Substitute it to the second equation:

          subtract 3 from both sides

      divide both sides by 3

If a = d and b = e and c = f then the system of equations has infinitely many solutions.

Example:

Change the signs in the second equation. Next add both sides of equations:

If  a = d and b = e and c ≠ f then the system of equations has no solution.

Example:

Change the signs in the second equation. Next add both sides of equations:

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step-by-step explanation: