# How do you solve the system of equations -8x - 8y = 8 and - 7x - 8y = 16 using elimination?

Mar 29, 2018

$x = 8$ and $y = - 9$

#### Explanation:

Both have -8y so we can eliminate it by adding equation:

$\quad \setminus \quad - 8 x - 8 y = 8$
$- \quad - 7 x - 8 y = 16$

$\quad \quad \setminus \setminus - x \quad \quad \quad \quad \quad \setminus = - 8$

Solving for x would get you $x = 8$.

Now plug this value into first equation:
$- 8 \left(8\right) - 8 y = 8$

$- 64 - 8 y = 8$

$- 8 y = 8 + 64$

$- 8 y = 72$

$y = - 9$

So we have $x = 8$ and $y = - 9$

Mar 29, 2018

$x = 8 , y = - 9$

#### Explanation:

$\left[\begin{matrix}- 8 x - 8 y & = & 8 \\ - 7 x - 8 y & = & 16\end{matrix}\right]$

multiply first row by $- 1$

$\left[\begin{matrix}8 x + 8 y & = & - 8 \\ - 7 x - 8 y & = & 16\end{matrix}\right]$

$\left(8 - 7\right) x + \left(8 - 8\right) y = - 8 + 16$

$1 x + 0 y = 8$

$x = 8$

Now, we can use any row to obtain $y$:

$8 x + 8 y = - 8$

Using $x = 8$:

$8 \textcolor{red}{\left(8\right)} + 8 y = - 8$

$64 + 8 y = - 8$

$8 y = - 8 - 64$

$8 y = - 72$

$y = - \frac{72}{8}$

$y = - 9$