Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
minus, x, plus, y, equals, 3
−x+y=
3
minus, 2, x, plus, 2, y, equals, 5
−2x+2y=
5

Answer 1

This system of equations has no solutions because if we multiply the first equation by 2, we get -2x + 2y = 6, which is different from the second equation -2x + 2y = 5. Since the two equations represent parallel lines that will never intersect, there are no solutions.