Solving Linear Systems by Linear Combinations
Rule 1: The solution of a system can be found by using an algebraic method called the Elimination Method. To find the set of solutions using the substitution method, we follow the steps listed below:
Step 1: Simplify and put both equations in the form Ax + By = C if needed.
Step 2: Multiply one or both equations by a number that will create opposite coefficients for either x or y if needed.
Step 3: Add equations.
Step 4: Solve for remaining variable.
Step 5: Solve for second variable.
Step 6: Check the proposed ordered pair solution in BOTH original equations.
Remark: Sometimes neither of the variables in a system of equations can be eliminated by simply adding or subtracting the equations. In this case, another method is to multiply one or both of the equations by some number so that adding or subtracting eliminates one of the variables.
Read the explanation below to learn more about solving linear systems by linear combinations.
Solving Linear Systems by Linear Combinations
Practice: Solve systems of equations by the elimination method using addition and subtraction below.