How do you solve this system of equations: -3x - 3y = 0 and - 3x - 10y = 14?

Dec 14, 2017

$x = 2$ and $y = - 2$

Explanation:

As $- 3 x - 3 y = 0$, $- 3 x = 3 y$

Putting this in $- 3 x - 10 y = 14$ we get

$3 y - 10 y = 14$

or $- 7 y = 14$

or $y = \frac{14}{- 7} = - 2$

and -3x=3×(-2)

or $- 3 x = - 6$

or $x = \frac{- 6}{- 3} = 2$

Hence $x = 2$ and $y = - 2$

Dec 14, 2017

x = 2 and y = -2

Explanation:

Given:

$- 3 x - 3 y = 0 \mathmr{and} - 3 x - 10 y = 14$

Let $- 3 x = 3 y$
Now, we substitute for $- 3 x$ in $- 3 x - 10 y = 14$, that is;

$3 y - 10 y = 14$
$- 7 y = 14$
$\textcolor{red}{y = - 2}$

Next, substitute the value of y in any one of the above equations to get the respective x value;

$- 3 x - 10 \left(- 2\right) = 14$
$- 3 x + 20 = 14$
$- 3 x = - 6$
$\textcolor{red}{x = 2}$

Therefore, $x = 2$ and $y = - 2.$

Dec 14, 2017

$x = 2 \mathmr{and} y = - 2$

Explanation:

Note that the terms in $x$ are the same in each equation.

Isolate the $x$ term, make it the subject in each equation.

$- 3 x = 3 y \text{ "and" } - 3 x = 10 y + 14$

We know that $- 3 x = - 3 x$, so equating the right sides gives:

$10 y + 14 = 3 y \text{ } \leftarrow$ now solve for $y$

$10 y - 3 y = - 14$

$7 y = - 14$

$y = - 2$

Use the value of $y$ to find $x$

$- 3 x = 3 \left(- 2\right)$

$- 3 x = - 6$

$x = 2$

Check in the second equation.

$- 3 x = 10 y + 14$

$- 3 \left(2\right) \text{ "and" } 10 \left(- 2\right) + 14$

$- 6 \text{ " and " } - 20 + 14$

$- 6 = - 6$