Related Pages Show The following steps show how to solve a System of Equations using the Addition or Elimination Method. Scroll down the page for examples and solutions.  In some word problems, we may need to translate the sentences into more than one equation. If we have two unknown variables then we would need at least two equations to solve the variable. In general, if we have n unknown variables then we would need at least n equations to solve the variable. There are two main methods to use when you need to solve more than one equation: Substitution Method and Addition Method. Check the coefficients"> of the variables. If the coefficient of one of the variables is 1 then use the Substitution Method otherwise use the Addition Method. In the Addition Method, the two equations are added together to eliminate one of the variables. We try to get the coefficients of one of the variables to be opposites so that addition will eliminate it. Let’s look at some examples for this free algebra tutorial. Example 1: Solution: Step 1: In this example the coefficients of y are already opposites (+3 and –3). Just add the two equations to eliminate y. Step 2:
Isolate variable x Step 3: To get the value of y you need to use the substitution method. Substitute x =
2 into <class=“highlight-label”> equation 1. Step 4: Isolate variable y Step 5: Check your answer with <class=“highlight-label”> equation 2 Answer: x = 2 and y = –2 Example 2: Solution: Step 1: In this example none of the coefficients are opposites. We need to multiply the equations with some numbers to get the coefficients opposite. Lets take the coefficients of y. Multiply each term of <class=“highlight-label”> equation 1 by 4 Multiply each term of <class=“highlight-label”>
equation 2 by 3 Step 2: Add the two equations to eliminate y. Step 3:
Isolate variable x Step 4: To get the value of y you need to use the substitution method. Substitute x =
2 into <class=“highlight-label”> equation 1. Step 5: Isolate variable y Step 6: Check your answer with <class=“highlight-label”> equation 2 Answer: x = 2 and y = –1 How to use the addition (Elimination) Method to solve a system of linear equations?Step 1: “Line up” the variables. Examples:
Solving a system of equations using the elimination (addition) method This example requires multiplying one equation by a constant.
System of Equations Using Elimination (No Solution) 5x + 2y = 4
System of Equations Using Elimination (Infinite Solutions) 2x - 5y = 4
Systems of Equations CalculatorThis tool will help you check your steps and answers when solving two equations in two variables. Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. How do you do addition elimination method?The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.
How do you solve a system of linear equations by adding or subtracting?To use the addition/subtraction method, do the following: Multiply one or both equations by some number(s) to make the number in front of one of the letters (unknowns) the same or exactly the opposite in each equation. Add or subtract the two equations to eliminate one letter. Solve for the remaining unknown.
What are the 3 methods for solving a system of equations?There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method.
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Solve the system of equations using the addition method
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