3x+3y=0 12x+2y=-20 Help!!!?

Question

This is the kind of question my teacher is asking but I do not understand how to do it. I thought that maybe if I heard it phrased differently it might help. I'm looking for a solution to this system of equations.

Answer 1

- 12x - 12y = 0
12x + 2y = - 20-----ADD

-10 y = - 20
y = 2

3x + 6 = 0
x = - 2

x = - 2 , y = 2

Answer 2

There are many ways to solve this. You could solve it by using substitution, combination, graphing, etc. I'll use substitution because it's probably the easiest to show.

3x + 3y = 0
12x + 2y = -20

First isolate one of the variables (either x or y) in ONE of the problems so it's either (1)x or (1)y, no coefficients. Since both coefficients of the y are smaller (or equal to), you should divide by the coefficient from the y.

(3x + 3y = 0)/3
OR
(12x + 2y = -20)/2

x + y = 0
OR
6x + y = -10

Now get the y by itself by subtracting the x.

y = -x + 0
OR
y = -6x - 10

Now substitute one of the "y equals" equations into one of your original equations.

Substitute y = -x+0 into 12x + 2y = -20:
12x + 2(-x + 0) = -20
12x - 2x = -20
10x = -20
x = -2
OR
Substitute y = -6x - 10 into 3x + 3y = 0:
3x + 3(-6x - 10) = 0
3x - 18x - 30 = 0
- 15x = 30
x = -2

So either way, x = -2. Now to find y, you plug in -2 for x in either of your original equations.

3(-2) + 3y = 0
-6 + 3y = 0
3y = 6
y = 2
OR
12(-2) + 2y = -20
-24 + 2y = -20
2y = 4
y = 2

Either way, y = 2.

So your answer is (-2,2). You should always phrase your answer as an ordered pair of (x,y).

Hope this helps!

Answer 3

x= -2, y=2

You need to either add or subtract the equations together, having either the numbers before either the x's or y's being the same or opposite numbers so you can make it a one variable equation, like this.

3x+3y=0
4(3x+3y)=4(0)
12x+12y = 0

12x+12y = 0
-12x+2y = -20
___________
0x + 10y = 20 (the 12x-12x=0, 12y-2y=10y, and 0-(-20)= 20)

10y=20
/10 /10
y=2

now subsitute this in for one of the orignal equations, and solve for x.

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

you could also of used the other equation (12x+2(2) = -20 leads to x= -2 also.)

and that is your answer, x= -2 and y =2

The reason that you can add or subtract the equations together is that you are adding/subtracting the same number from each side; since you know that 12x+2y= -20, they can be added/subtracted to an equation just like you could subtract 3 or add 5 to any equation.

Answer 4

3x+3y=0 4(3x+3y)=0 12x+12y=0
12x+2y=20 12x+2y=20 12x+2y=20


0x+10y=-20
10y=-20
y=-2

Answer 5

you mean like a linear equation? we just haad midterms today lol but anyways
3x+3y=0
isolate the y
so minus 3x from both sides so its
3x=0-3x aka just -3x
so its 3y=-3x and divide the by three to get the y by its self
so its y= -3x/3
y=-1x
so the slope is negative and rise of one run of one. the y intercept is 0,0 and there is ur equation of the line in slope-intercept form. the other one try to do by urself
good luck

Answer 6

3x = -3y
x = -y

12(-y) + 2y = -20
-12y + 2y = -20
-10y = -20
y = 2

x = -2

(-2,2)
Check:

3(-2) +3(2) = 0 and 12(-2) + 2(2) = -20
-6 + 6 = 0 and -24 + 4 = -20
0 = 0 and -20 = -20

they check out

Answer 7

Think the teach is trying to get you into the concept of neg. #
or the concept of 0. [anything times 0= 0]
From the given the answer is varible.x and y could be anything
EX.....(.3x[-1] )+ (3x1)=0
(3x0) +(3x0) =0

Answer 8

3x+3y=0

you can ge t

x=-y

then

12x+2y=-20

because x=-y so y=-x

2y=-2x

12x+2y=12x-2x=10x=-20
so x=-2
y=-x=2

Answer 9

3x+3y=0
12x+2y=-20

Multiply first eq by 4 and subtract from second eq.
  12x+2y=-20
-(12x+12y=0)
------------------
-10y = -20

Solve for y:
-10y = -20
y = 2

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

Answer 10

Im guessing these are simultaneous equations?