How do u solve a system of equations?

Question

How do u solve this system of equations?

-x + 3y = 0
2x + 6y = 12



thank u =]

Answer 1

a good way would be through substitutions:
so:
-x + 3y = 0
so: x = 3y

substituting:
2(3y) + 6y = 12
6y +6y = 12
y = 1

Answer 2

In solving a system of equations, we want to be able to add or subtract terms to make the equation less complex. In order to do this it is easiest to pick a variable, x or y, and make sure that both equations variables have the same absolute value, but with opposite signs. In your example we have:

-x+3y=0
2x+6y=12

We can choose to work with our x or y variable in this case since both are not insanely complex. I would choose to work with the y variable because they are both products of the number 3. In this case we want our top equation's y value to have a coefficient of -6. In order to achieve this we must multiply the entire equation by -2:

(-2)(-x+3y)=(-2)(0)
(2x-6y)=0

We can now add the equations together:

2x-6y=0
2x+6y=12

We have: 2x+2x+6y-6y=0+12
4x=12

Now we solve for x:
x=(12/4)
x=3

Because we have an x value, we can now plug out value back into either equation to find the y value:

-(3)+3y=0
-3+3y=0
3y=0+3
3y=3
y=(3/3)
y=1

We now have the point pair (3,1). To check this pair we must plug it into both equations. If the equations are true, we have successfully solved the system of equations:

(-3)+3(1)=0
-3+3=0
0=0

So far so good...

2(3)+6(1)=12
6+6=12
12=12

Voila!

Answer 3

Multiply 1st equation by 2 getting -2x +6y = 0
Now add this result to the 2nd equation getting 12y=12
so y=1
Now put y=1 in 1st equation getting -x+3*1= 0 so x = 3

Answer 4

Double the first equation, and add it to the second.
See, doubling both sides of the first equation is a legal operation.
And if since both sides are equal, adding the left side of the first equation to both sides of the second is the same as adding the left to the left and the right to the right.
That probably made no sense, but that way, the x's will cancel, you can solve for the y's and substitute back in to find the x.

Answer 5

Solve one equation for either x or y and then plug it into the other equation.