{3x+2y=6 {x+y=0?

Question

please show work thank you so very much :)

Answer 1

If you want to find the solution of the two:

from the second you have x = -y

Then

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

So then x = -y = 6

(6,-6)

Answer 2

Have you tried using a matrix? It's my favorite way to solve systems of equations.

Make a matrix like this for the two equations:

[3 2 | 6]
[1 1 | 0]

Then simplify as follows:

1. Switch the two rows:
[1 1 | 0]
[3 2 | 6]

2. Multiply the top row by -3 and add it to the bottom row to get rid of the 3 in the x position:
[1 1 | 0]
[0 -1| 6]

3. Multiply the bottom row by -1 to get rid of the negative:
[1 1 | 0]
[0 1 | -6]

4. Multiply the bottom row by -1 and add it to the top row to get rid of the 1 in the y position:
[1 0 | 6]
[0 1 | -6]

5. Since you have simplified the matrix into a form where there is a 1 in the x position in the first row and a 1 in the y position of the second row and zeros everywhere else, your solution is what is on the right hand side of the matrix. So the solution is x = 6, y = -6 or (6, -6).



Another way to solve it besides the substitution method or the matrix method is to use a graphing calculator. Solve both equations for y. So you will have y = -x and y = -3/2 x + 3. Graph the two equations and then use the intersect function under the graph menu to find where the two lines intersect. This intersection point is the answer to your system. It will be at the point (6, -6).

Hope that helps. Good luck.

Answer 3

x = 6 - 2y replace into different equation 3x + 2y = 6 will become: 3(6 - 2y) + 2y = 6 18 - 6y + 2y = 6 18 - 4y = 6 18 - 6 = 4y 12 = 4y y = 3 placed back in first equation x + 2(3) =6 x + 6 = 6 x = 0 so y =3 and x = 0, then you definately can continually plug the numbers into each and each equation to learn your artwork

Answer 4

The second equation tells you that y = -x, so in the first equation you replace y by -x and get

3x + 2*(-x) = 6. I guess you can finish it from there.

Another method is to think of how you can make the y term the same in both equations. Since the first has 2y in it, we multiply the second by 2 and get 2x + 2y = 0. So we are looking at

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

Now subtract the left sides and the right sides. 3x - 2x = x, 2y-2y=0, and 6-0=6, and so we have
x = 6

Sub that in the second equation to get 6 + y = 0
and so y = -6

Answer 5

Okay,

you know these two equations:
3x+2y=6 (Eqn 1)
&
x+y=0 (Eqn 2)

x=-y (from Eqn 2)
Insert -y into x for Equation 1

3(-y)+2y=6
-y=6 therefore y=-6 and x=6 (from Eqn 2)

Answer 6

3x+2y=6
x+y=0 multiply by -2
-2x-2y=0
3x+2y=6 add
x=6
x+y=0
6+y=0 subtract 6 from each side
y=-6
solution is (6, -6)

check
3*6+2*(-6)=6
18-12=6
6=6

Answer 7

3x+2y=6.....(1)
x+y=0.........(2)
(2) : x= -y
put (2) into (1) :3(-y)+2y=6
-3y+2y=6
-y=6
so, y= -6

then insert (y= -6)into (2) : x+(-6)=0
x - 6 =0
x =6
finally the ans is..... x=6 ; y= -6 q(",)p so easy!!

Answer 8

Subtract x from both sides:
y=-x

Substitute it in the next equation:
3x+2(-x)=6

3x-2x=6
x=6

6+y=0
y=-6

The solution set is (6,-6)

Check:
3(6)+2(-6)=6
18-12=6
6=6

6-6=0
0=0

Answer 9

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

x = -y
x = -6
Solution: {x,y elements of R | x = -6; y = 6}
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