SOLUTION: Solve by graphing. 3x + y = 13 x + 6y = -7

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Question 87257: Solve by graphing.
3x + y = 13
x + 6y = -7
Answer by jim_thompson5910(35256) 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%2By=13

1x%2B6y=-7





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%2By=13 Start with the given equation



1y=13-3x Subtract 3+x from both sides



1y=-3x%2B13 Rearrange the equation



y=%28-3x%2B13%29%2F%281%29 Divide both sides by 1



y=%28-3%2F1%29x%2B%2813%29%2F%281%29 Break up the fraction



y=-3x%2B13 Reduce



Now lets graph y=-3x%2B13 (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%2B13%29+ Graph of y=-3x%2B13




So let's solve for y on the second equation


1x%2B6y=-7 Start with the given equation



6y=-7-x Subtract +x from both sides



6y=-x-7 Rearrange the equation



y=%28-x-7%29%2F%286%29 Divide both sides by 6



y=%28-1%2F6%29x%2B%28-7%29%2F%286%29 Break up the fraction



y=%28-1%2F6%29x-7%2F6 Reduce





Now lets add the graph of y=%28-1%2F6%29x-7%2F6 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B13%2C%28-1%2F6%29x-7%2F6%29+ Graph of y=-3x%2B13(red) and y=%28-1%2F6%29x-7%2F6(green)


From the graph, we can see that the two lines intersect at the point (5,-2) (note: you might have to adjust the window to see the intersection)