Question

How many solutions does this system of equations have? 2x+y=1 4x+2y=2 A.none B.exactly one C.exactly two D.infinitely many

Answer 1

`2x+y=1 \\4x+2y=2|:2\\\\ 2x+y=1\\ 2x+y=1\\`

both equations are identical ⇒ D

Answer 2

Given the equations 2x+y=1 and 4x+2y=2, if we divide the second equation by 2, we are left with 2x+y=1, which is the same equation as the first. This means that the lines over lap, and that there are infinite places where they "intercept"
Final answer:
D. Infinitely many