We are given a system of two linear equations with two variables, $x$ and $y$: $16x + 6y = -10$ $8x - 7y = -15$ 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 $y$:

$16x + 6y = -10$

$8x - 7y = -15$

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

2. Solution Steps

We can solve this system of equations using either substitution or elimination. Let's use elimination.

First, we can divide the first equation by 2 to simplify it:

$8x + 3y = -5$

Now we have the following system of equations:

$8x + 3y = -5$

$8x - 7y = -15$

We can eliminate $x$ by subtracting the second equation from the first equation:

$(8x + 3y) - (8x - 7y) = -5 - (-15)$

$8x + 3y - 8x + 7y = -5 + 15$

$10y = 10$

$y = \frac{10}{10}$

$y = 1$

Now that we have found the value of $y$, we can substitute it into either of the original equations to solve for $x$. Let's use the simplified first equation:

$8x + 3y = -5$

$8x + 3(1) = -5$

$8x + 3 = -5$

$8x = -5 - 3$

$8x = -8$

$x = \frac{-8}{8}$

$x = -1$

Therefore, the solution to the system of equations is $x = -1$ and $y = 1$.

3. Final Answer

x = -1, y = 1