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: \[2x + y = 1\] \[3x - y = 4\]
2. Add the two equations together to eliminate the variable \(y\) because \(y\) and \(-y\) will cancel out: \[(2x + y) + (3x - y) = 1 + 4\]
3. Simplify the resulting equation to combine like terms: \[2x + 3x + y - y = 5\] which simplifies to \[5x = 5\]
4. Solve for \(x\) by dividing both sides of the equation by 5: \[x = \frac{5}{5}\]
5. Substitute the value of \(x\) back into one of the original equations (for example, \$2x + y = 1\() to solve for \)y\(: \[2(\text{value of } x) + y = 1\] Then isolate \)y$ and solve.