Educator

Solving by Multiplication

• Sometimes you cannot get a solution by just adding or subtracting the original equations. You must first multiply one or both of the equations by appropriate constants to produce two new equations that have the same or opposite coefficients for one of the variables. Then you can add or subtract the new equations to eliminate the variable with the same or opposite coefficients. The resulting equation in one variable can be easily solved using familiar techniques. Then find the solution for the other variable by substituting the value for the first variable into either of the original equations.

• Use this method if none of the coefficients is 1 or –1 and neither pair of coefficients of the same variable are the equal or opposites.