SOLUTION: solve this system of equation by graphing 1. 3x-6y=-9 2x-4y=-6 2. x+y=-6 -x+2y=6

Algebra ->  Systems-of-equations -> SOLUTION: solve this system of equation by graphing 1. 3x-6y=-9 2x-4y=-6 2. x+y=-6 -x+2y=6       Log On


   

Question 126955: solve this system of equation by graphing
1. 3x-6y=-9
2x-4y=-6
2. x+y=-6
-x+2y=6

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1. 3x-6y=-9
2x-4y=-6
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


3x-6y=-9

2x-4y=-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


3x-6y=-9 Start with the given equation



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



-6y=-3x-9 Rearrange the equation



y=%28-3x-9%29%2F%28-6%29 Divide both sides by -6



y=%28-3%2F-6%29x%2B%28-9%29%2F%28-6%29 Break up the fraction



y=%281%2F2%29x%2B3%2F2 Reduce



Now lets graph y=%281%2F2%29x%2B3%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%2B3%2F2%29+ Graph of y=%281%2F2%29x%2B3%2F2




So let's solve for y on the second equation


2x-4y=-6 Start with the given equation



-4y=-6-2x Subtract 2+x from both sides



-4y=-2x-6 Rearrange the equation



y=%28-2x-6%29%2F%28-4%29 Divide both sides by -4



y=%28-2%2F-4%29x%2B%28-6%29%2F%28-4%29 Break up the fraction



y=%281%2F2%29x%2B3%2F2 Reduce





Now lets add the graph of y=%281%2F2%29x%2B3%2F2 to our first plot to get:


Graph of y=%281%2F2%29x%2B3%2F2(red) and y=%281%2F2%29x%2B3%2F2(green)


From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.



2. x%2By=-6
-x%2B2y=6

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



Start with the given system of equations:


1x%2By=-6

-x%2B2y=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


1x%2By=-6 Start with the given equation



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



1y=-x-6 Rearrange the equation



y=%28-x-6%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%28-6%29%2F%281%29 Break up the fraction



y=-x-6 Reduce



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




So let's solve for y on the second equation


-x%2B2y=6 Start with the given equation



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



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



y=%28%2Bx%2B6%29%2F%282%29 Divide both sides by 2



y=%28%2B1%2F2%29x%2B%286%29%2F%282%29 Break up the fraction



y=%281%2F2%29x%2B3 Reduce





Now lets add the graph of y=%281%2F2%29x%2B3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x-6%2C%281%2F2%29x%2B3%29+ Graph of y=-x-6(red) and y=%281%2F2%29x%2B3(green)


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