The resulting equation has one variable for which you can solve. It requires you to solve for one of the variables and substitute the result into the other equation. The substitution method, on the other hand, is a completely algebraic method. If we have a choice, we typically avoid this method in favor of the more accurate algebraic techniques. When the coordinates of the solution are not integers, the method is practically unusable. One drawback of this method is that it is very inaccurate. The simultaneous solution (−1, 10) corresponds to the point of intersection. The goal is to arrange that either the x terms or the y terms are opposites, so that when the equations are added, the terms eliminate. Typically, we have to find an equivalent system by applying the multiplication property of equality to one or both of the equations as a means to line up one of the variables to eliminate. Of course, the variable is not always so easily eliminated. This leaves us with a linear equation with one variable that can be easily solved:Īt this point, we have the x-coordinate of the simultaneous solution, so all that is left to do is back substitute to find the corresponding y-value. We can add the equations together to eliminate the variable y. But sometimes Substitution can give a quicker result. This method depends on the addition property of equations If A, B, C, and D are algebraic expressions, where A = B and C = D, then A + C = B + D.: given algebraic expressions A, B, C, and D we have Once you get used to the Elimination Method it becomes easier than Substitution, because you just follow the steps and the answers appear.

or addition method Often used when referring to the elimination method for solving systems.

In this section, the goal is to review another completely algebraic method for solving a system of linear equations called the elimination method A means of solving a system by adding equivalent equations in such a way as to eliminate a variable.

System by substitution