Question

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?

Answer 1

Well two lines intersect at 1 point, infinite points(they are the same), or don't intersect(they are parallel).

Answer 2

The point you find is probably the right point.

Answer 3

(4,1)

Answer 4

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

Answer 5

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

Answer 6

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.

Answer 7

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.

Answer 8

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?

Answer 9

(4,1) is my first point after solving for X and Y

Answer 10

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
|
|

Answer 11

You can do the same with the second line.

Answer 12

WAIT sorry y=-3! so it will be below the x-axis.

Answer 13

I hate to seem like an idiot but how did you get the -3 exactly?

Answer 14

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

Answer 15

This gave me the intersecting point. Now I need to find the other points to know which way my two lines are going.

Answer 16

a

Answer 17

Ha don't say that. I am probably explaining badly

Answer 18

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.

Answer 19

so the first line will go through (0,-3) (3,0) and (4,1)

Answer 20

ok I understand now. Thanks for your help. I just got a little stuck.

Answer 21

No problem!