Solve by graphing. If there isn't a unique solution to the system, state the reason. x-y=3 x+y=5 Please explain how to solve. I was only able to find one point which I understand is the answer but how do I find the other points to determine where my lines are on the graph?

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Solve by graphing. If there isn't a unique solution to the system, state the reason. x-y=3 x+y=5 Please explain how to solve. I was only able to find one point which I understand is the answer but how do I find the other points to determine where my lines are on the graph?

Mathematics
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Well two lines intersect at 1 point, infinite points(they are the same), or don't intersect(they are parallel).
The point you find is probably the right point.
(4,1)

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You should graph each line separately, be putting it in standard form if you like y = mx + b. and put in the intercepts and what not
But I need to know how to get the rest of the points to figure out what type of lines I have. ex: consistent, dependent, inconsistent
What do you mean by that? Two lines in a plane, will only intersect at most one point. Or they will be the same line. Or if they are parallel they will never intersect.
To graph it, you can take the first line and make it y = x - 3. Find the intercepts: by setting y = 0, solving for x. Then set x=0, solving for y. Plot these points and draw a line between them. That will be your first line.
Ok I have the point on the graph. Which way do you draw the line? I can draw the line in many directions. How do I find point 2 to give me the direction of my line?
(4,1) is my first point after solving for X and Y
So we will take the first line x - y = 3. Set y=0 and find that x = 3. | |<---- y=3 when x = 0 -------- <---- x=3 when y= 0 | |
You can do the same with the second line.
WAIT sorry y=-3! so it will be below the x-axis.
I hate to seem like an idiot but how did you get the -3 exactly?
I solved the equation like this: x-y=3 x+y=5 add both equations 2x=8 Y's cancel and then divide both sides by 2 x=4 Then I did the same thing only cancelling the X's and then solved for Y getting Y=1
This gave me the intersecting point. Now I need to find the other points to know which way my two lines are going.
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Ha don't say that. I am probably explaining badly
You did that perfectly. We can now just draw the lines. We can get -y =3 because x - y =3; x=0 (0) -y =3.
so the first line will go through (0,-3) (3,0) and (4,1)
ok I understand now. Thanks for your help. I just got a little stuck.
No problem!

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