SOLUTION: Solve by graphing: y=x+6, y=-3X+6

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Question 936548: Solve by graphing:
y=x+6, y=-3X+6
Found 2 solutions by TimothyLamb, MathLover1:
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
y = x + 6
y = -3x + 6
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put the system of linear equations into standard form
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x - y = -6
-3x - y = -6
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copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = 0
y = 6
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this system can also be solved by observation:
both equations have the same y-intercept = (0,6)
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graphing:
y = x + 6 (red)
y = -3x + 6 (green)
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+graph%28+300%2C+200%2C+-5%2C+5%2C+-2%2C+8%2C+x-y%2B6%2C+-3x-y%2B6%29+
---
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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

y=x%2B6
y=-3x%2B6
______________________
-x%2By=6
3x%2By=6
______________________

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-x%2By=6

3x%2By=6





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


-x%2By=6 Start with the given equation



1y=6%2Bx Add +x to both sides



1y=%2Bx%2B6 Rearrange the equation



y=%28%2Bx%2B6%29%2F%281%29 Divide both sides by 1



y=%28%2B1%2F1%29x%2B%286%29%2F%281%29 Break up the fraction



y=x%2B6 Reduce



Now lets graph y=x%2B6 (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%2B6%29+ Graph of y=x%2B6




So let's solve for y on the second equation


3x%2By=6 Start with the given equation



1y=6-3x Subtract 3+x from both sides



1y=-3x%2B6 Rearrange the equation



y=%28-3x%2B6%29%2F%281%29 Divide both sides by 1



y=%28-3%2F1%29x%2B%286%29%2F%281%29 Break up the fraction



y=-3x%2B6 Reduce





Now lets add the graph of y=-3x%2B6 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B6%2C-3x%2B6%29+ Graph of y=x%2B6(red) and y=-3x%2B6(green)


From the graph, we can see that the two lines intersect at the point (0,6) (note: you might have to adjust the window to see the intersection)