Answer
The solution to this system of equations is $(-2, -5)$.
Work Step by Step
In the first equation, we already have an expression for $y$ that we can substitute into the second equation to find $x$. Let us do the substitution:
$3x - (2x - 1) = -1$
Use distributive property to get rid of the parentheses:
$3x - 2x + 1 = -1$
Substract $1$ from both sides to isolate constants to the right side of the equation:
$3x - 2x = -2$
$x = -2$
Now that we have a value for $x$, we can substitute it into the first equation to solve for $y$:
$y = 2(-2) -1$
$y = -4 -1$
$y = -5$
The solution to this system of equations is $(-2, -5)$.
Let us substitute these values into the second equation to see if the equation holds true:
$3(-2) - (-5) = -1$
$-6 + 5 = -1$
$-1 = -1$
This statement is true; therefore, the solution is correct.