Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
3, x, plus, 2, y, equals, 4
3x+2y=
4
minus, 6, x, minus, 4, y, equals, minus, 8
−6x−4y=
−8
Answer

Answer 1

Infinitely many solutions.

Reason: the second equation is -2 times the first (−2(3x+2y)=−6x−4y=−8), so both equations are the same line. The solution set is all (x,y) with 3x+2y=4, e.g. y = (4−3x)/2 (or parametrize x = t, y = (4−3t)/2).