SOLUTION: I know these questions are easy for you guys but I just don't retain any algebra at all. I try my best before I consult you. On that note can you help me refresh my memory on this

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Question 128750: I know these questions are easy for you guys but I just don't retain any algebra at all. I try my best before I consult you. On that note can you help me refresh my memory on this graphing type problem? I need to solve by graphing.
Do I need points for this question? If I do I will use x = points 0 ,-1, 1 and
Do I need points for Y ? Can you show me the easiest way? I really appreciate all your help, I really do! This problem is a handout and is not in a book. Thanks so much.
x-2y=0 and 2x-y= -3
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Let's graph the first equation x-2y=0

Let's find a point using x=0

x-2y=0 Start with the first equation

0-2y=0 Plug in x=0

-2y=0 Simplify

y=0%2F-2 Divide both sides by -2 to isolate y

y=0 Reduce

So when x=0, y=0. So our first point is (0,0)





Let's find another point using x=1

x-2y=0 Start with the first equation

1-2y=0 Plug in x=1

-2y=-1 Subtract 1 from both sides

y=-1%2F-2 Divide both sides by -2 to isolate y

y=1%2F2 Reduce


So when x=1, y=1%2F2. So our second point is



Now plot the points and



drawing%28500%2C500%2C-9%2C11%2C-9%2C11%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-9%2C11%2C0%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C0%2C0.1%29%2C%0D%0Acircle%280%2C0%2C0.12%29%2C%0D%0Acircle%280%2C0%2C0.15%29%2C%0D%0Acircle%281%2C1%2F2%2C0.1%29%2C%0D%0Acircle%281%2C1%2F2%2C0.12%29%2C%0D%0Acircle%281%2C1%2F2%2C0.15%29%0D%0A%29+



Now draw a straight line through the two points. This line is the graph of x-2y=0

drawing%28500%2C500%2C-9%2C11%2C-9%2C11%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-9%2C11%2C%281%2F2%29x%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C0%2C0.1%29%2C%0D%0Acircle%280%2C0%2C0.12%29%2C%0D%0Acircle%280%2C0%2C0.15%29%2C%0D%0Acircle%281%2C1%2F2%2C0.1%29%2C%0D%0Acircle%281%2C1%2F2%2C0.12%29%2C%0D%0Acircle%281%2C1%2F2%2C0.15%29%0D%0A%29+ Graph of x-2y=0 through the two points and







Let's graph the second equation 2x-y=+-3

Let's find a point using x=0

2x-y=+-3 Start with the second equation

2%280%29-y=+-3 Plug in x=0

-y=-3 Simplify

y=-3%2F-1 Divide both sides by -1 to isolate y

y=3 Reduce

So when x=0, y=3. So our first point is (0,3)





Let's find another point using x=1

2x-y=+-3 Start with the second equation

2%281%29-y=+-3 Plug in x=1


2-y=+-3 Multiply


-y=-5 Subtract 2 from both sides

y=-5%2F-1 Divide both sides by -1 to isolate y

y=5 Reduce


So when x=1, y=5. So our second point is (1,5)




Now plot the points and



drawing%28500%2C500%2C-9%2C11%2C-9%2C11%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-9%2C11%2C0%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C3%2C0.1%29%2C%0D%0Acircle%280%2C3%2C0.12%29%2C%0D%0Acircle%280%2C3%2C0.15%29%2C%0D%0Acircle%281%2C5%2C0.1%29%2C%0D%0Acircle%281%2C5%2C0.12%29%2C%0D%0Acircle%281%2C5%2C0.15%29%0D%0A%29+



Now draw a straight line through the two points. This line is the graph of 2x-y=+-3

drawing%28500%2C500%2C-9%2C11%2C-9%2C11%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-9%2C11%2C%28-3-2x%29%2F%28-1%29%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C3%2C0.1%29%2C%0D%0Acircle%280%2C3%2C0.12%29%2C%0D%0Acircle%280%2C3%2C0.15%29%2C%0D%0Acircle%281%2C5%2C0.1%29%2C%0D%0Acircle%281%2C5%2C0.12%29%2C%0D%0Acircle%281%2C5%2C0.15%29%0D%0A%29+ Graph of 2x-y=+-3 through the two points and



Now simply graph these two line together to get

drawing%28500%2C500%2C-9%2C11%2C-9%2C11%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-9%2C11%2C%28-3-2x%29%2F%28-1%29%2C%281%2F2%29x%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C3%2C0.1%29%2C%0D%0Acircle%280%2C3%2C0.12%29%2C%0D%0Acircle%280%2C3%2C0.15%29%2C%0D%0Acircle%281%2C5%2C0.1%29%2C%0D%0Acircle%281%2C5%2C0.12%29%2C%0D%0Acircle%281%2C5%2C0.15%29%2C%0D%0Acircle%280%2C0%2C0.1%29%2C%0D%0Acircle%280%2C0%2C0.12%29%2C%0D%0Acircle%280%2C0%2C0.15%29%2C%0D%0Acircle%281%2C1%2F2%2C0.1%29%2C%0D%0Acircle%281%2C1%2F2%2C0.12%29%2C%0D%0Acircle%281%2C1%2F2%2C0.15%29%2C%0D%0Ablue%28circle%28-2%2C-1%2C0.1%29%29%2C%0D%0Ablue%28circle%28-2%2C-1%2C0.12%29%29%2C%0D%0Ablue%28circle%28-2%2C-1%2C0.15%29%29%0D%0A%29+ Graph of x-2y=0 (green) and 2x-y=+-3 (red)


From the graph, we can see that the two lines intersect at the point (-2,-1) (blue point)