SOLUTION: Solve the system x+2y=0 3x-y=3 This is what I did, but I am unsure if it is correct so far: x+2y=0 -2y -2y x=-2y 3(-2y)-y=3 -6y-y=3 -7y=3 y=3/-7

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system x+2y=0 3x-y=3 This is what I did, but I am unsure if it is correct so far: x+2y=0 -2y -2y x=-2y 3(-2y)-y=3 -6y-y=3 -7y=3 y=3/-7      Log On


   

Question 910319: Solve the system
x+2y=0
3x-y=3
This is what I did, but I am unsure if it is correct so far:
x+2y=0
-2y -2y
x=-2y
3(-2y)-y=3
-6y-y=3
-7y=3
y=3/-7
Found 3 solutions by rothauserc, MathLover1, solver91311:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
We are given:
x+2y=0
3x-y=3
use second equation and solve for y
add y to both sides of =, then subtract
3 from both sides of =
y = 3x-3
substitute for y in first equation
x + 2*(3x-3) = 0
x + 6x - 6 = 0
7x = 6
x = 6/7
now substitute for x in second equation
3*(6/7) - y = 3
18/7 - y = 3
add y to both sides of = and subtract 21/7 (3)
from both sides of =
y = -3/7
solution set is x = 6/7 and y = -3/7
now check the answers
substitute in first equation
x+2y=0
6/7 + 2*(-3/7) = 0
6/7 -6/7 = 0
0 = 0
substitute in second equation
3x-y=3
3*(6/7) - (-3/7) = 3
18/7 + 3/7 = 3
21/7 = 3
3 = 3
our answers for x and y check :-)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=3%2F-7 or y=-3%2F7 ..correct
all you need to do is go to any equation, plug in y value and solve for x


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



Start with the given system of equations:


1x%2B2y=0

3x-y=3





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%2B2y=0 Start with the given equation



2y=0-x Subtract +x from both sides



2y=-x%2B0 Rearrange the equation



y=%28-x%2B0%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%280%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B0 Reduce



Now lets graph y=%28-1%2F2%29x%2B0 (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+%28-1%2F2%29x%2B0%29+ Graph of y=%28-1%2F2%29x%2B0




So let's solve for y on the second equation


3x-y=3 Start with the given equation



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



-y=-3x%2B3 Rearrange the equation



y=%28-3x%2B3%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%283%29%2F%28-1%29 Break up the fraction



y=3x-3 Reduce





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


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F2%29x%2B0%2C3x-3%29+ Graph of y=%28-1%2F2%29x%2B0(red) and y=3x-3(green)


From the graph, we can see that the two lines intersect at the point (6%2F7,-3%2F7) (note: you might have to adjust the window to see the intersection)

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Spot on, so far. Now all that is necessary is to substitute back into either one of the original equations and solve for . You will have easier arithmetic if you use the first one, but, given correct arithmetic, you get the same answer either way.

John

My calculator said it, I believe it, that settles it