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

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)   (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)   (Show Source): You can put this solution on YOUR website!
or ..correct
all you need to do is go to any equation, plug in value and solve for

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

Start with the given system of equations:

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

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

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

Answer by solver91311(24713)   (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

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