Question

Please Help!!

Answer 1

@Cardinal_Carlo

Answer 2

Where is d

Answer 3

But first which number do we know is correct

Answer 4

@Nerdsarecool there is no D

Answer 5

If a system has an infinite number of solutions, it is dependently consistent. If it only has one solution, it is independently consistent. Otherwise, if it has no solution, then it is considered inconsistent.

Let's take a look at the first system:
\[x + 5y = -2\]
\[x + 5y = 4\]
If you rewrite these equations into point-slope form, you'll see that:
\[m = -\frac{ 1 }{ 5 }\]
However, each equation's y-intercept is different from the other. This indicates that these lines are parallel to each other but are a distance apart. Meaning, we won't find a single solution. We can therefore conclude that this system is inconsistent.

Answer 6

Oh okay would the 2nd one be B?

Answer 7

Well, coincidence refers to a system of equations where both equations are identical to each other. This is not the case for the second system.

We see in the first equation that:
\[m = 3\]
And in the second equation that:
\[m = 2\]
Furthermore, they both have the same y-intercept:
\[b = 4\]
Meaning, that these two equations intersect at point (0, 4). Since there is only one solution for this system, we can conclude that this is a independently consistent system.

Answer 8

If you're looking for coincidence, observe the third system of equations. Notice how they're basically the same line. Of course, you'd have to put the second equation into point-slope form first in order to get a clearer view.

Answer 9

Try identifying the fourth system for fun. You're smart. I know you can do it @narissa.

Answer 10

okay ill try thank you

Answer 11

You're welcome

Answer 12

i think the lats one is C @Cardinal_Carlo

Answer 13

last*

Answer 14

You got close. Well, it was a good try.

Notice in the first equation:
\[m = -\frac{ 2 }{ 5 }\]
But on the second equation:
\[m = \frac{ 2 }{ 5 }\]
Notice how the first equation has a positive slope while the second has a negative slope. This would mean that these two would cross only once. Therefore, we would call this one an independently consistent system.

Answer 15

To make it simple just follow these rules:

Same line = coincident
One intersection = consistent independent
No intersections = inconsistent

And to see how the lines interact with each other, try rewriting them in point-slope form. Or better yet, graph them.

Answer 16

thank u

Answer 17

You're welcome