SOLUTION: Solve the system of equations by graphing x-2y=10 x+2y=-2

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Question 462938: Solve the system of equations by graphing
x-2y=10
x+2y=-2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x-2y=10
x%2B2y=-2
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x-2y=10

1x%2B2y=-2





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-2y=10 Start with the given equation



-2y=10-x Subtract +x from both sides



-2y=-x%2B10 Rearrange the equation



y=%28-x%2B10%29%2F%28-2%29 Divide both sides by -2



y=%28-1%2F-2%29x%2B%2810%29%2F%28-2%29 Break up the fraction



y=%281%2F2%29x-5 Reduce



Now lets graph y=%281%2F2%29x-5 (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+%281%2F2%29x-5%29+ Graph of y=%281%2F2%29x-5




So let's solve for y on the second equation


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



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



2y=-x-2 Rearrange the equation



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



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



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





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


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x-5%2C%28-1%2F2%29x-1%29+ Graph of y=%281%2F2%29x-5(red) and y=%28-1%2F2%29x-1(green)


From the graph, we can see that the two lines intersect at the point (4,-3) (note: you might have to adjust the window to see the intersection)