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

• A. $\left(-1,1\right)$
• B. $\left(1,1\right)$
• C. $\left(1,-1\right)$
• D. $\left(-1,-1\right)$

Answer: (C)

Verified step by step guidance

1. Start by writing down the system of equations: \(2x + y = 1\) and \(3x - y = 4\).
2. To use the elimination method, add the two equations together to eliminate \(y\). This means adding \(2x + y = 1\) and \(3x - y = 4\).
3. When you add the equations, the \(y\) terms cancel out, resulting in \(5x = 5\).
4. Solve for \(x\) by dividing both sides of the equation \(5x = 5\) by 5, which gives \(x = 1\).
5. 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 \(y = -1\).