SOLUTION: Solve the linear system by graphing. X+2y=1 -2x+y=-4 When I solved this problem I got (2,-1/2), but I don't think I did the problem correctly. Thank you!

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Question 1022398: Solve the linear system by graphing.
X+2y=1
-2x+y=-4
When I solved this problem I got (2,-1/2), but I don't think I did the problem correctly.
Thank you!

Found 4 solutions by Alan3354, Edwin McCravy, josgarithmetic, jim_thompson5910:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Solve the linear system by graphing.
X+2y=1
-2x+y=-4
When I solved this problem I got (2,-1/2), but I don't think I did the problem correctly.
------------------
Why do you think that?

Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!
You must be very accurate when you solve a system of equations
by graphing. You must use graph paper with large squares and 
use a ruler.

Make a table of points for each line:

 x | y      x | y
 1 | 0      1 |-2 
 3 |-1      3 | 2
-1 | 1     -1 |-6


Plot those points and draw lines through them, using
graph paper and a ruler:



So you see the lines cross at a point that has fractions for both
coordinates.  It's a good idea to draw a vertical and a horizontal
line (in red below) to the x and y-axis, like this:


 

It looks like the x coordinate is a little less than 2,
but not close enough to be 1.9, so I'd guess x = 1.8.
The y coordinate is a little less than halfway to -1,
which would be -0.5, but closer to -0.5 than the other 
was to 2, so I'd guess that it is y = -0.4

That's the best you can do with graphing.

Edwin





Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
, the same system.


This graph might be distorted, but appears to show intersection about (2,-1/2).

Solving can start algebraically by equating the two formulas for y.





THIS SHOULD SUGGEST THAT THE INTERSECTION POINT ON THE GRAPH IS NOT DISTORTED. The x-coordinate is actually a little less than 2, being . The point is a little difficult to read on the graph.

Continue with algebra to find the y-coordinate to help understand what you see on graph. , simply .

Maybe you can find this clearer on paper, but intersection is ( 9/5, -2/5 ).

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
It's not the correct answer. You can check by going back to the original equations and plugging in the (x,y) solution point. It makes the first equation true, but the second equation is false when you replace x with 2 and y with -1/2

==============================================================================================================

Here is one way to solve the system


Step 1) Solve for x







-------------------------------------------------------------------

Step 2) Move onto the second equation. Replace every copy of 'x' with '1-2y'



Replaced x with 1-2y





Notice how x is gone now. There is only one variable left. Let's solve for y


-------------------------------------------------------------------

Step 3) Solve for y















-------------------------------------------------------------------


Step 4) We'll use this value of y to find x




Replaced y with -0.4






The solution to the system of equations is (x,y) = (1.8, -0.4)


==============================================================================================================

Let's check the answer


Checking the first equation

Replaced (x,y) with (1.8, -0.4)



Checking the second equation

Replaced (x,y) with (1.8, -0.4)




Since BOTH equations are true, this confirms the solution (1.8, -0.4)

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