Answer
$G$
Work Step by Step
We are asked to solve this system of equations with the elimination method.
First, we rewrite the equations so that the variables are on one side while the constant is on the other:
$2x - y = 4$
$3x + y = 1$
We see that in the two equations, the $y$ term is exactly the same except they have opposite signs. If we add these two equations together, we can eliminate the variable $y$ and just deal with one variable instead of two:
$2x = 4$
$3x = 1$
Now, we can add the two equations together to come up with one single equation:
$5x = 5$
Divide each side by $5$ to solve for $x$:
$x = 1$
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:
$2(1) - y = 4$
Multiply to simplify:
$2 - y = 4$
Now, we subtract $2$ from both sides of the equation to isolate constants to the right side of the equation:
$-y = 2$
Divide both sides by $-1$ to solve for $y$:
$y = -2$
The solution to this system of equations is $(1, -2)$. This corresponds to option G.
