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. First, write 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 is possible because the coefficients of y are +1 and -1.
3. Add the equations: (2x + y) + (3x - y) = 1 + 4. This simplifies to 5x = 5.
4. Solve for x by dividing both sides of the equation by 5, resulting in 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.