How do I solve for the elimination method: 5x + 3y= -7 and 7x - 2y =13 (step 1); 10x + 6y =-14 and 21x -6y = 39 ( step 2), 31x/31= 25/31, x= 25/31 (step 4). But after that I get lost. Can somebody help me out please.

Of course! I can help you with solving the system of equations using the elimination method step-by-step. Let's go through the process together:

Step 1:
We have the following system of equations:
5x + 3y = -7
7x - 2y = 13

To solve this system, we need to eliminate one variable by adding or subtracting the equations. In this case, we can eliminate the "y" variable by multiplying the first equation by 2 and the second equation by 3, such that the coefficients of "y" will cancel each other out:

(2) * (5x + 3y) = (2) * (-7) --> 10x + 6y = -14
(3) * (7x - 2y) = (3) * (13) --> 21x - 6y = 39

So, our new system of equations becomes:
10x + 6y = -14 (equation 1)
21x - 6y = 39 (equation 2)

Step 2:
Now, let's add equation 1 and equation 2 in order to eliminate the "y" variable:

10x + 6y + 21x - 6y = -14 + 39
(10x + 21x) + (6y - 6y) = 25
31x + 0 = 25
31x = 25

Step 3:
Next, we need to isolate the variable "x" by dividing both sides of the equation by 31:

31x/31 = 25/31
x = 25/31

Step 4:
Now that we have found the value of "x", we need to substitute it back into one of the original equations to find the value of "y". Let's choose the first equation:

5x + 3y = -7
5(25/31) + 3y = -7
125/31 + 3y = -7

Step 5:
To solve for "y", we can isolate it by subtracting 125/31 from both sides of the equation:

125/31 + 3y - 125/31 = -7 - 125/31
3y = -7 - 125/31

Step 6:
To simplify the right side of the equation, we need to find a common denominator:

3y = -7 - 125/31
3y = -7 * 31/31 - 125/31
3y = (-217 - 125)/31
3y = -342/31

Step 7:
Now, divide both sides of the equation by 3 to solve for "y":

(3y)/3 = (-342/31)/3
y = -342/31 * 1/3
y = -342/93
y = -38/31

So, the solution to the system of equations is x = 25/31 and y = -38/31.

10 x + 6 y = -14 yes

21 x - 6 y = 39 yes
add those two
31 x + 0 = 25
so
x = -25/31 yes
Now go back and use -25/31 in either of the original equations to get y
5 (-25/31) + 3 y = -7
3 y = 125/31 -7
3 y = (125-217)/31
y = - 92/3