When should you use multiplication to solve a system of linear equations by elimination?

You should use multiplication to solve a system of linear equations by elimination when the coefficients of one variable in the two equations are not easily aligned for direct elimination. This often occurs when the coefficients are not opposites or when they are not easily manipulated to create a zero in one of the variables. By multiplying one or both equations by a suitable value, you can create equal or opposite coefficients, allowing you to eliminate one variable and solve the system more efficiently.