How do you solve the system of equations -6x + 5y = - 5 and 10x - 10y = 20?

1 Answer
Jun 6, 2018

$x = - 5$ and $y = - 7$.

Explanation:

For this system of equations, I would adjust the first equation so that when you add the two equations together, the $y$ is eliminated.

You can do so by multiplying everything by $2$:

$\left(- 6 x + 5 y = - 5\right) \text{ } \times 2$

$- 12 x + 10 y = - 10$

Now that this equation has a positive $10 y$ and the other equation has a $- 10 y$, adding the two problems would eliminate the $y$ variable.

$\left\{\begin{matrix}- 12 x + 10 y = - 10 \\ 10 x - 10 y = 20\end{matrix}\right.$

Added together:

$- 2 x = 10$

You can now solve for $x$ by dividing both sides by $- 2$.

$x = - 5$

Now you can take any of the equations and enter in $- 5$ for $x$ to solve for $y$.

$- 6 \left(- 5\right) + 5 y = - 5$

Multiply the $- 6$ and $- 5$

$30 + 5 y = - 5$

Subtract $30$ from both sides

$5 y = - 35$

Divide both sides by $5$

$y = - 7$

There are many ways to solve systems of equations, but often it's easiest to find a way to adjust one of the equations so that when you add them together they eliminate one of the variables.