We are asked to solve the following system of equations using the elimination method: $ -5x + 2y = -15 $ $ x - 2y = 3 $

1. Problem Description

We are asked to solve the following system of equations using the elimination method:

$-5x + 2y = -15$

$x - 2y = 3$

2. Solution Steps

We can solve the system of equations by elimination. We observe that the $y$ terms have opposite signs in the two equations. Thus, we can directly add the two equations to eliminate $y$.

$(-5x + 2y) + (x - 2y) = -15 + 3$

$-5x + x + 2y - 2y = -12$

$-4x = -12$

Dividing both sides by $-4$, we get

$x = \frac{-12}{-4}$

$x = 3$

Now, we substitute the value of $x$ into the second equation to find the value of $y$:

$x - 2y = 3$

$3 - 2y = 3$

$-2y = 3 - 3$

$-2y = 0$

$y = \frac{0}{-2}$

$y = 0$

Thus, the solution to the system of equations is $x = 3$ and $y = 0$.

3. Final Answer

The solution is $x = 3$ and $y = 0$.

The solution as an ordered pair is $(3, 0)$.