Solving Linear Systems by Substitution
The solution of a system can be found by using an algebraic method called the Substitution Method. To find the set of solutions using the substitution method, we follow the steps listed below:
Step 1: Simplify if needed (removing ( ) and removing fractions)
Step 2: Solve one equation for either variable.
Step 3: Substitute what you get for step 2 into the other equation.
Step 4: Solve for the remaining variable.
Step 5: Solve for second variable.
Step 6: Check the proposed ordered pair solution in BOTH original equations.
Remark:
- If your variable drops out and you have a FALSE statement that means your answer is no solution.
- If your variable drops out and you have a TRUE statement that means your answer is infinite solutions, which would be the equation of the line.
To find out more about solving linear systems by substitution by reading the explanation below.
Solving Linear Systems by Substitution
Practice: Solve systems of equations by the substitution method in the following exercises below.
Solving Linear Systems by Substitution 1