Solve by the elimination method.

2r-5s = -11
5r + 2s = 16

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To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations.

Looking at the given equations:
Equation 1: 2r - 5s = -11
Equation 2: 5r + 2s = 16

We will eliminate the variable "s." To do that, we will multiply Equation 1 by 2 and Equation 2 by 5, so that the coefficients of "s" will cancel each other out when we add the equations.

Multiplying Equation 1 by 2, we get:
4r - 10s = -22 ---> (Equation 3)

Multiplying Equation 2 by 5, we get:
25r + 10s = 80 ---> (Equation 4)

Now, we can add Equation 3 and Equation 4 to eliminate "s":
(4r - 10s) + (25r + 10s) = (-22) + 80

Simplifying the equation:
4r + 25r - 10s + 10s = 58

Combining like terms:
29r = 58

Now, we can solve for "r" by dividing both sides of the equation by 29:
r = 58/29
r = 2

Now that we have the value of "r," we can substitute it back into either Equation 1 or Equation 2 to solve for "s." Let's use Equation 1:
2(2) - 5s = -11

Simplifying the equation:
4 - 5s = -11

Rearranging the equation to isolate "s":
-5s = -11 - 4
-5s = -15

Solving for "s" by dividing both sides of the equation by -5:
s = (-15)/(-5)
s = 3

Therefore, the solution to the system of equations is r = 2 and s = 3.