Question

The following system of equations is _____.

y = -1/3x +2/3
2x + 6y = 4

A) independent
B) equivalent
C) inconsistent

Answer 1

Vocab:
independent ⇒ one solution
equivalent ⇒ same solution
inconsistent ⇒ no solution

y = -1/3x + 2/3
2x + 6y = 4
Plug in y into the equation 2x + 6y = 4.

2x + 6(-1/3x + 2/3) = 4
Solve for x.

2x - 2x + 4 = 4
4 = 4

4 = 4, so that means there are an infinite number of solutions.
The answer should be a dependent system of equations. A dependent system of equations has an infinite number of solutions.
Answer B) is the closest, as it means they have the same solution = infinite solutions.