Question

How many solutions does the system of equations have?





A.
The system has exactly one solution.


B.
The system has infinitely many solutions.


C.
The system has no solution.

Answer 1

@Hero how do you find this out?

Answer 2

You look at the graphs of x - y = -4 and y = 2:

If they intersect at one point, then there is one solution.
If they never intersect at any point, then there is zero solution.
If they intersect at every point, then there is infinite solution.

Answer 3

so it would be infinite solution?

Answer 4

@Hero

Answer 5

How many times do the graph of both lines intersect? https://www.desmos.com/calculator/xgzh9ms7ip

Answer 6

3?

Answer 7

Not exactly. What about if I post it this way...
https://www.desmos.com/calculator/vhjfzmjlgh
Now how many times do they intersect?

Answer 8

1 so it would be one solution

Answer 9

Yes, you finally have it. When it comes to the graphs of two linear equations, there will either be zero, one, or two solutions in accordance with what I described above.

Answer 10

You are only concerned with the intersection of the lines of interest, not with any other lines.

Answer 11

ok thank you!