Answer:
B. consistent and dependent.
Explanation:
y = -3x – 1
{
3x + y = -1
__________
This system is consistent and dependent because it has an infinite amount of solutions.
The easiest way to tell if the solutions are infinite is if the equations are equivalent.
As you can see, 3x + y = -1 is standard form, while y = -3x – 1 slope-intercept form.
We can tell that they are equivalent by converting the standard form equation to slope-intercept to see that they are equivalent.
All you need to do is subtract both sides by 3x to get the equation with respect to y so that it is slope intercept.
3x + y = -1 → 3x – 3x + y = -1 – 3x → y = -3x – 1.
[y = -3x – 1] = [y = -3x – 1].
Independent = one solution pair.
Inconsistent = no solution pair.
Consistent = at least one solution.
Dependent = infinite solutions.