Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
4, x, plus, y, equals, 2
4x+y=
2
minus, 4, x, minus, y, equals, minus, 2
−4x−y=
−2

Answer 1

The second equation is just −1 times the first (−(4x+y)=−2). So the two equations are dependent and represent the same line. There are infinitely many solutions.

General solution: y = 2 − 4x, i.e. (x,y) = (t, 2−4t) for any real t.