What is the difference between elimination by addition and elimination by substitution methods when solving systems of equations?
The elimination method and the substitution method are two common methods used to solve systems of equations. Here's an explanation of the difference between elimination by addition and elimination by substitution:
1. Elimination by Addition:
- Also known as the elimination by the addition method or the method of addition.
- In this method, you add or subtract the equations in a way that eliminates one of the variables when the two equations are added or subtracted.
- The goal is to end up with a new equation that only involves one variable, allowing you to solve for that variable easily.
- Once you've found the value of one variable, you substitute it back into one of the original equations to find the value of the other variable.
2. Elimination by Substitution:
- Also known as the substitution method.
- In this method, you solve one equation for one variable, and then substitute that expression into the other equation.
- The substitution is done in a way that the new equation only contains one variable, making it easier to solve.
- Once you've found the value of one variable, you substitute it back into one of the original equations to find the value of the other variable.
The main difference between the two methods lies in how they handle the variables. In elimination by addition, you manipulate the equations using addition or subtraction to eliminate a variable. In elimination by substitution, you solve one equation for a variable and substitute it into the other equation to eliminate a variable.
Both the elimination by addition and elimination by substitution methods are effective techniques for solving systems of equations. The choice between the two methods can depend on the specific system of equations and personal preference.