Use the elimination method to solve the following system of linear equations.
$2x+y=1$
$3x-y=4$

$$\left$(-1,1$\right$)$

$$\left$(1,1$\right$)$

$$\left$(1,-1$\right$)$

$$\left$(-1,-1$\right$)$

Verified step by step guidance

Start by writing down the system of equations: $2x + y = 1$ and $3x - y = 4$.

To use the elimination method, add the two equations together to eliminate $y$. This means adding $2x + y = 1$ and $3x - y = 4$.

When you add the equations, the $y$ terms cancel out, resulting in $5x = 5$.

Solve for $x$ by dividing both sides of the equation $5x = 5$ by 5, which gives $x = 1$.

Substitute $x = 1$ back into one of the original equations, for example $2x + y = 1$, to find $y$. This gives $2(1) + y = 1$, which simplifies to $y = -1$.

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Use the elimination method to solve the following system of linear equations.
$2x+y=1$
$3x-y=4$