SOLUTION: what is the graphical form of this equation. 2x-y=3 x+2y=4

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Question 100722: what is the graphical form of this equation.
2x-y=3
x+2y=4
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


2x-y=3

1x%2B2y=4





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


2x-y=3 Start with the given equation



-y=3-2x Subtract 2+x from both sides



-y=-2x%2B3 Rearrange the equation



y=%28-2x%2B3%29%2F%28-1%29 Divide both sides by -1



y=%28-2%2F-1%29x%2B%283%29%2F%28-1%29 Break up the fraction



y=2x-3 Reduce



Now lets graph y=2x-3 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x-3%29+ Graph of y=2x-3




So let's solve for y on the second equation


1x%2B2y=4 Start with the given equation



2y=4-x Subtract +x from both sides



2y=-x%2B4 Rearrange the equation



y=%28-x%2B4%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%284%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B2 Reduce





Now lets add the graph of y=%28-1%2F2%29x%2B2 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x-3%2C%28-1%2F2%29x%2B2%29+ Graph of y=2x-3(red) and y=%28-1%2F2%29x%2B2(green)


From the graph, we can see that the two lines intersect at the point (2,1) (note: you might have to adjust the window to see the intersection)