Elimination method:

x+5y=-13
2x-5y=-19

( , )

Add the two equations to eliminate y, or

x+2x=-13+(-19)
x=-32/3
Find y by substitution.

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To solve the system of equations using the elimination method:

1. Start with the given equations:
x + 5y = -13 (Equation 1)
2x - 5y = -19 (Equation 2)

2. We will eliminate one variable by adding or subtracting the two equations. In this case, we can eliminate the 'y' variable by adding the two equations together.

(x + 5y) + (2x - 5y) = (-13) + (-19)
Simplifying the left side: 3x + 0y = -32
Simplifying the right side: 3x = -32

3. Now, isolate the variable 'x' by dividing both sides of the equation by 3:
3x/3 = -32/3
x = -32/3

4. Substitute the value of 'x' back into one of the original equations (Equation 1 or Equation 2) to solve for 'y'. Let's use Equation 1:

x + 5y = -13 (Equation 1)
(-32/3) + 5y = -13

5. Simplify the equation and solve for 'y':
Multiply both sides of the equation by 3 to eliminate the fraction:
3 * ((-32/3) + 5y) = 3 * (-13)
-32 + 15y = -39
Add 32 to both sides:
-32 + 32 + 15y = -39 + 32
15y = -7
Divide both sides of the equation by 15:
15y/15 = -7/15
y = -7/15

6. So, the solution to the system of equations is:
x = -32/3
y = -7/15

Therefore, the solution to the system of equations is (x, y) = (-32/3, -7/15).

To use the elimination method, you need to eliminate one variable from the two equations by adding or subtracting the equations. Let's solve the system of equations:

1) Add the two equations together: (x+5y) + (2x-5y) = (-13) + (-19)
This simplifies to: 3x = -32

2) Divide both sides of the equation by 3 to solve for x: 3x/3 = -32/3
x = -32/3

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y.

Let's substitute x = -32/3 into the first equation:
(-32/3) + 5y = -13

3) Solve for y by isolating the variable:
5y = -13 + 32/3
5y = (-39 + 32)/3
5y = -7/3

4) Divide both sides of the equation by 5 to get the value of y:
y = (-7/3) / 5
y = -7/15

Therefore, the solution to the system of equations is (x , y) = (-32/3 , -7/15).