Question

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?

y = -2x + 4

6x + 3y =

-12
-4
4
12

Answer 1

So when we want infinitely many solutions, we want to have basically the same equation

So like if you have

x + y = 5

Then to get another line that would have the same solutions, we just multiply it by any number on both sides

So like
2x + 2y = 10
3x + 3y = 15

Answer 2

Do you understand that?

Basically multiplying the same number on both sides still keeps the equation the same because we could always simplify it by taking out that common factor

And so then we get infinitely many solutions because they're both basically the same thing and they intersect each other at every single point because they're the same line and so they overlap

Answer 3

So for your question, first get them to look similar so bring the 2x to the other side and you have

2x + y = 4

And the other equation is

6x + 3y = ??

So what should the number be in place of ??

What number did we multiply the first equation by to get that second equation

Answer 4

not sure

Answer 5

Reread what I wrote and tell me where you get lost :)

You know how we have a line and we can draw it on graphing paper?
Now we can draw any other line and if it cross the line, like imagine an x. That center part where they intersect would be the solution of those two lines.

Now you could draw a line that's parallel to your first one and then those two lines would never intersect. They would never cross each other. Thus they would have no solutions.

And finally if you drew the same line on top of your original line then it has the same exact points in common and therefore has infinitely many solutions because the line could be stretching forever and ever going in that direction