Determine whether the following systems have one solution, no solution, or infinite solutions

Question

3x-y=7

-6x+2y=-14

Answer 1

Infinite solutions. Equation 2 is just equation 1 multiplied by -2. That means the system really consists of just a single equation in two unknowns. All we can say about x & y is that:

y = 3x - 7

Pick any x you want and this tells you y, but because you can pick any x, there are infinitely many solutions.