Solving Systems by Substitution

Topics for Today:

We are still working on solving systems of equations and introduced a new method today that uses algebra instead of graphing.  We have discussed the limitations of the graphing method, and why we might use algebra instead.  There are three algebraic methods used to solve systems:  substitution method, elimination method, and the matrix method.  We will learn and practice the first two; solving of matrices with systems of 2 or more equations is covered in Algebra II.

The general process for solving systems algebraically is the same.  First, we solve for one of the variables; then we substitute that solution into one of our equations to find the second variable.

For the substitution method, we follow this process:

1. In the original system, see if one variable is isolated; if not, then isolate a variable. 
2. Substitute the expression into the second equation.
3. Solve the equation for the first variable.
4. Substitute the solution found in step 3 into one of the original equations to solve for the other variable. 
5. Identify the solution as an ordered pair.
6. Check both original equations to ensure the solution works for both. 

(Graphic Credit: https://www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/solve-by-substitution.php)

Vocabulary:  substitution method

Sections Covered in Textbook:

7-2: Solving Systems Using Substitution (pages 347-351)

Resources & Tutorials:

1) How to solve a system using substitution method.
2) Solving Systems of Equations by Substitution.
3) Solving Systems Using Substitution Class notes