Question

how many solutions does the system of eqations have. x-y=-4 and y=2 (-4,4) and (0,2)

Answer 1

A.
The system has exactly one solution.







B.
The system has infinitely many solutions.







C.
The system has no solution

Answer 2

(-4,4) and (0,2)?

Answer 3

yes

Answer 4

What are these? Solution?

Answer 5

no that's where the lines are on the graph

Answer 6

x-y=-4 and y=2 these are the solutions

Answer 7

?????????????

Answer 8

anyone?

Answer 9

So whatcha got to do is quite simply, notice how one of the equations is simply\[y=2\]well, if you plug that into the other equation\[x-y=-4\]you'll get a resulting x-value, as for how to tell if there is one, none, or infinitely many solutions, first step is to look at the slope of the lines since you're dealing with straight lines.
If they have equal slope, they are parallel and will have infinitely many solutions if they are actually the SAME line.
They have no solutions if they are parallel with a different b value when you have them in the form\[y=mx+b\]and they have one solution if you get a simple number when you do substitution, which is finding where the lines cross eachother

Answer 10

If you need a further explanation of anything feel free to ask, i'll try my best

Answer 11

ok and what would be the steps,

Answer 12

because I understand what you where saying I just don't get how I would plug it in

Answer 13

so you have\[y=2\]plug that into your other equation X-Y=-4, so you'd have\[X-Y=-4\]\[X-(2)=-4\]add that 2 to both sides to get the X alone and you have that X=-2, so you know they intersect at one point for sure

Answer 14

and in fact, if you understand that they are both lines, then that has to be the only intersection

Answer 15

Unless they have same slope, of course

Answer 16

okay, so it would be (-2)-y=-4 and (-2)-2=-4 right embryo?

Answer 17

?

Answer 18

No no no, don't replug in the new X-value that you found, once you find the point of intersection, that is your answer, so your final answer would be something along the lines of, "These lines have one point of intersection at (-2,2), and therefore there is only one solution"

Answer 19

oh okay so there would be only one solution in the end

Answer 20

Yes that is correct, it's easy to think about it if you draw a bunch of different lines on a paper, and extend those lines until they cross eachother, if they have the same slope, they can never cross, if they have the same slope and the same y-intercept (so they are the same line) then they have infinitely many solutions, if they have different slopes, they have exactly 1 solution

Answer 21

okay thatnk you so much for the clear explanation, it really helped and I get it now! :)

Answer 22

and can you maybe help me with another one?

Answer 23

and can you maybe help me with another problem?

Answer 24

Go ahead and make a new post (so close this one and ask as a new question) since i currently have to go somewhere, but if it's still unanswered when i get back (in about 30 minutes) i can take a crack at it

Answer 25

ok thank you so much!!!! :)