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. Write down the system of equations clearly: \[2x + y = 1\] \[3x - y = 4\]
2. Add the two equations together to eliminate the variable \(y\). When you add them, the \(y\) terms (\(+y\) and \(-y\)) will cancel out, leaving an equation with only \(x\).
3. Solve the resulting equation for \(x\). This will give you the value of \(x\).
4. Substitute the value of \(x\) back into one of the original equations (either one works) to solve for \(y\).
5. Write the solution as an ordered pair \((x, y)\) representing the point where the two lines intersect.