Elimination Method....I am not understanding this method either and need some help here is what I am working on:

1)
x+8y=33
-x+4y=3

2)
5x+5y=-7
7x-2y=13

3)
0.3x-0.2y=4
0.5x+0.3y=-7/17

Can someone please help me with these!

in this method you are trying to get the coefficients of one set of variables to be either the same or opposites.

If you get them to be the same, you would then subtract the two equations from each other, and if they are opposite, you would add the equations.

I will do the second
looking at the y's, I notice it would be nice if they were both 10, so
multiply the first by 2 ----> 10x + 10y = -14
multiply the second by 5 --> 35x - 10y = 65
add them ----> 45x = 51
x = 51/45 = 17/15
sub that back into the "easier" original equations
I pick #2 , in this case it doesn't make much difference
7(17/15) - 2y = 13
-2y = 13 - 119/15
y = -38/15

do the others the same way

I am still confused on number one because it starts with the same variable so I don't really know where to start can you help....?

I am also confused as to how to work the fraction part of number 3 can you help?

Sure, I can help you understand the elimination method. The elimination method is a way to solve a system of linear equations by eliminating one of the variables. Here are the steps to solve a system of equations using the elimination method:

1) Look at the coefficients of one of the variables in both equations. Choose a variable and determine if you need to multiply one or both equations by some number(s) so that the coefficients of that variable will be additive inverses (i.e., they will cancel each other out when added together).
2) Add or subtract the equations to eliminate one of the variables. This will result in a new equation with only one variable.
3) Solve the new equation for the remaining variable.
4) Substitute the value obtained in step 3 back into one of the original equations to find the value of the other variable.
5) Check your solution by substituting the values of the variables obtained in step 3 and 4 into both original equations. The solution should satisfy both equations.

Now, let's solve the equations you provided using the elimination method:

1) x + 8y = 33
-x + 4y = 3

To start, let's eliminate the x variable. Notice that the coefficients of x are already additive inverses (-1 and 1), so we can directly add the equations together:
(x + 8y) + (-x + 4y) = 33 + 3
12y = 36
Now, we can solve for y by dividing both sides of the equation by 12:
y = 36/12
y = 3

To find the value of x, substitute the value of y back into one of the original equations. Let's use the first equation:
x + 8(3) = 33
x + 24 = 33
x = 33 - 24
x = 9

Therefore, the solution to this system of equations is x = 9 and y = 3.

2) 5x + 5y = -7
7x - 2y = 13

In this case, we can eliminate the y variable by multiplying the first equation by 2 and the second equation by 5 to make the coefficients of y additive inverses:
2(5x + 5y) = 2(-7) (multiply the first equation by 2)
5(7x - 2y) = 5(13) (multiply the second equation by 5)

Simplifying the equations, we get:
10x + 10y = -14
35x - 10y = 65

Now, add the equations together to eliminate y:
(10x + 10y) + (35x - 10y) = -14 + 65
45x = 51
Divide both sides of the equation by 45:
x = 51/45
Simplify the fraction if possible:
x = 17/15

To find the value of y, substitute the value of x back into one of the original equations. Let's use the first equation:
5(17/15) + 5y = -7
17/3 + 5y = -7
To get rid of the fraction, multiply the entire equation by 15:
15(17/3 + 5y) = 15(-7)
17(5) + 15(5y) = -105
85 + 75y = -105
Subtract 85 from both sides:
75y = -190
Divide both sides by 75:
y = -190/75
Simplify the fraction if possible:
y = -38/15

Therefore, the solution to this system of equations is x = 17/15 and y = -38/15.

3) 0.3x - 0.2y = 4
0.5x + 0.3y = -7/17

To eliminate the decimal coefficients, multiply the first equation by 10 and the second equation by 15 to make all coefficients integers:
10(0.3x - 0.2y) = 10(4) (multiply the first equation by 10)
15(0.5x + 0.3y) = 15(-7/17) (multiply the second equation by 15)

Simplifying the equations, we get:
3x - 2y = 40
7.5x + 4.5y = -105/17

To eliminate the decimal coefficients, we can multiply both equations by 2 and 17 respectively to make the coefficients integers:
2(3x - 2y) = 2(40) (multiply the first equation by 2)
17(7.5x + 4.5y) = 17(-105/17) (multiply the second equation by 17)

Simplifying the equations again, we get:
6x - 4y = 80
127.5x + 76.5y = -105

Now, to eliminate the decimal coefficients, we can multiply the first equation by 3 and the second equation by 2 to make the coefficients integers:
3(6x - 4y) = 3(80) (multiply the first equation by 3)
2(127.5x + 76.5y) = 2(-105) (multiply the second equation by 2)

Simplifying the equations, we get:
18x - 12y = 240
255x + 153y = -210

Now, let's eliminate the y variable. Multiply the first equation by 17 and the second equation by 12:
17(18x - 12y) = 17(240) (multiply the first equation by 17)
12(255x + 153y) = 12(-210) (multiply the second equation by 12)

Simplifying the equations, we get:
306x - 204y = 4080
3060x + 1836y = -2520

Add the equations to eliminate y:
(306x - 204y) + (3060x + 1836y) = 4080 + (-2520)
3366x = 1560
Divide both sides of the equation by 3366:
x = 1560/3366
Simplify the fraction if possible:
x = 260/561

To find the value of y, substitute the value of x back into one of the original equations. Let's use the first equation:
0.3(260/561) - 0.2y = 4
78/561 - 0.2y = 4
To get rid of the fraction, multiply the entire equation by 561:
561(78/561 - 0.2y) = 561(4)
78 - 112.2y = 2244
Subtract 78 from both sides:
-112.2y = 2166
Divide both sides by -112.2:
y = 2166/-112.2
Simplify the fraction if possible:
y = -81/4.2
Simplify the fraction further or convert to a decimal if needed.

Therefore, the solution to this system of equations is x = 260/561 and y = -81/4.2 (or as a decimal, if needed).