SOLUTION: i need help with this question 3x-y=6 x+2y=2 I have to solve the systems of equations by graphing

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Question 672689: i need help with this question
3x-y=6
x+2y=2
I have to solve the systems of equations by graphing
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:


3x-y=6

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


3x-y=6 Start with the given equation



-y=6-3x Subtract 3+x from both sides



-y=-3x%2B6 Rearrange the equation



y=%28-3x%2B6%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%286%29%2F%28-1%29 Break up the fraction



y=3x-6 Reduce



Now lets graph y=3x-6 (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+3x-6%29+ Graph of y=3x-6




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%2B2 Rearrange the equation



y=%28-x%2B2%29%2F%282%29 Divide both sides by 2



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



y=%28-1%2F2%29x%2B1 Reduce





Now lets add the graph of y=%28-1%2F2%29x%2B1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x-6%2C%28-1%2F2%29x%2B1%29+ Graph of y=3x-6(red) and y=%28-1%2F2%29x%2B1(green)


From the graph, we can see that the two lines intersect at the point (2,0) (note: you might have to adjust the window to see the intersection)