SOLUTION: 3x-6y=9 4x-2y=24

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Question 116962:
3x-6y=9 4x-2y=24
Found 2 solutions by MathLover1, checkley71:
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-6y=9

4x-2y=24





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-6y=9 Start with the given equation



-6y=9-3x Subtract 3+x from both sides



-6y=-3x%2B9 Rearrange the equation



y=%28-3x%2B9%29%2F%28-6%29 Divide both sides by -6



y=%28-3%2F-6%29x%2B%289%29%2F%28-6%29 Break up the fraction



y=%281%2F2%29x-3%2F2 Reduce



Now lets graph y=%281%2F2%29x-3%2F2 (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-3%2F2%29+ Graph of y=%281%2F2%29x-3%2F2




So let's solve for y on the second equation


4x-2y=24 Start with the given equation



-2y=24-4x Subtract 4+x from both sides



-2y=-4x%2B24 Rearrange the equation



y=%28-4x%2B24%29%2F%28-2%29 Divide both sides by -2



y=%28-4%2F-2%29x%2B%2824%29%2F%28-2%29 Break up the fraction



y=2x-12 Reduce





Now lets add the graph of y=2x-12 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x-3%2F2%2C2x-12%29+ Graph of y=%281%2F2%29x-3%2F2(red) and y=2x-12(green)


From the graph, we can see that the two lines intersect at the point (7,2) (note: you might have to adjust the window to see the intersection)

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
I WILL ASSUME YOUWANT TO SOLVE THIS SET OF EQUATION BY GRAPHING!!!!!!
3X-6Y=9 OR -6Y=-3X+9 OR Y=-3X/-6+9/-6 OR Y=X/2-3/2 (RED LINE)
4X-2Y=24 OR -2Y=-4X+24 OR Y=-4X/-2+24/-2 OR Y=2X-12 (GREEN LINE)
+graph%28+300%2C+200%2C+-6%2C+15%2C+-20%2C+10%2C+y+=+x%2F2+-3%2F2%2C+y+=+2x+-12%29+ (graph 300x200 pixels, x from -6 to 15, y from -20 to 10, of TWO functions y = x/2 -3/2 and y = 2x -12).
IT WOULD SEEM THAT THE SOLUTION IS (7,2)