SOLUTION: Solve graphically x-y=3, 2x-y=4

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Question 1010988: Solve graphically x-y=3, 2x-y=4
Answer by MathLover1(20850) 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:


1x-y=3

2x-y=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


1x-y=3 Start with the given equation



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



-y=-x%2B3 Rearrange the equation



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



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



y=x-3 Reduce



Now lets graph y=x-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+x-3%29+ Graph of y=x-3




So let's solve for y on the second equation


2x-y=4 Start with the given equation



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



-y=-2x%2B4 Rearrange the equation



y=%28-2x%2B4%29%2F%28-1%29 Divide both sides by -1



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



y=2x-4 Reduce





Now lets add the graph of y=2x-4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-3%2C2x-4%29+ Graph of y=x-3(red) and y=2x-4(green)


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