Elimantion tnethod \( 2 x-y=-1 \times 1 \) \( x-2 y=4 \times 2 \) \( -2 x-y=-1 \) \( 2 x-4 y=8 \) \( -y--4 y=-1-8 \) \( -y+4 y-9 \) \( y=-3 \)

The elimination method is a powerful technique for solving systems of linear equations. It involves eliminating one variable by combining equations, allowing you to solve for the remaining variable. In your example, you correctly manipulated the equations to isolate \(y\). Once \(y\) is found, you substitute it back into one of the original equations to find \(x\). A common mistake when using the elimination method is to miscalculate when combining equations. It's crucial to keep track of signs and coefficients! For example, watch out for sign errors like the switch from \( -y + 4y \) to \( -y - 4y \). Double-checking arithmetic and maintaining systematic setup helps ensure accuracy—after all, math should be fun, not frustrating!