We are given a system of two linear equations with two variables $x$ and $y$: $5x - 3y = 15$ $2x + y = -5$ We need to solve for $x$ and $y$.

1. Problem Description

We are given a system of two linear equations with two variables $x$ and $y$:

$5x - 3y = 15$

$2x + y = -5$

We need to solve for $x$ and $y$.

2. Solution Steps

We can use the substitution or elimination method to solve this system of equations. Let's use the substitution method. From the second equation, we can express $y$ in terms of $x$:

$y = -5 - 2x$

Now, substitute this expression for $y$ into the first equation:

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

$5x + 15 + 6x = 15$

$11x + 15 = 15$

$11x = 0$

$x = 0$

Now, substitute $x = 0$ back into the equation for $y$:

$y = -5 - 2(0)$

$y = -5$

Therefore, the solution to the system of equations is $x = 0$ and $y = -5$.

3. Final Answer

$x = 0, y = -5$