Answer
$G$
Work Step by Step
First, we need to rewrite the equations so that the variables are on one side while the constants are on the other. Let's look at the first equation:
$-3x - y = -1$
We can divide both sides by $-1$ to get an equation that is easier to work with:
$3x + y = 1$
Let's convert the second equation:
$x + 2y = -2$
Let's put the two equations together:
$3x + y = 1$
$ x + 2y = -2$
We need to convert the equations so that one of the variables in both equations are exactly the same, except they have opposite signs. Then we can come up with one single equation to work with. Let's multiply the first equation by $-2$:
$-2(3x + y) = -2(1)$
Simplify:
$-6x - 2y = -2$
Let's add this equation to the second equation:
$-6x - 2y = -2$
$ x + 2y = -2$
The $-2y$ and $2y$ cancel each other out, so we are only left with one equation containing the $x$ variable when we add them together:
$-5x = -4$
Divide each side by $-5$ to solve for $x$:
$x = \frac{4}{5}$
Now that we have the value for $x$, we can plug it into one of the equations to solve for $y$. Let's plug in the value for $x$ into the first equation:
$-y = 3(\frac{4}{5}) - 1$
Multiply first, according to order of operations:
$-y = \frac{12}{5} - 1$
Now, we subtract to simplify. First, we need to convert $1$ into a fraction with $5$ as the denominator:
$-y = \frac{12}{5} - \frac{5}{5}$
Subtract to simplify:
$-y = \frac{7}{5}$
Divide both sides by $-1$ to solve for $y$:
$y = - \frac{7}{5}$
The solution to this system of equations is $\left(\frac{4}{5}, - \frac{7}{5}\right)$. This corresponds to option G.
