Final answer:
To eliminate 'x' using the subtraction method in a system of equations, the coefficients of 'x' in both equations must be the same. Ensuring to always perform operations equally on both sides maintains the integrity of the equation.
Step-by-step explanation:
When solving a system of equations using the subtraction method to eliminate 'x', the coefficients of the variable 'x' must be the same (or opposite) in both equations. To achieve this, you may need to multiply one or both equations by a number to get the same coefficient for 'x' in each equation. Once the coefficients are equal, you subtract one equation from the other which will eliminate 'x' from the system, allowing you to solve for the other variable.
It is crucial that any operation, whether it is addition, subtraction, multiplication or division, is applied to both sides of an equation. By maintaining this balance, the expression remains an equality. This ensures that the equation stays valid and solvable.