SLE - Solve Systems of Two Linear Equations by Substitution Lesson

Substitution Method

In the previous lesson, we learned that a system of linear equations is a set of equations of straight lines composed of 2 or more equations.  We also learned how to use the graphing method to solve for the solution to a system.  Sometimes, it is difficult to identify the exact solution to a system of equations by graphing and it will be necessary to solve the system using another method.  In this lesson, we will learn to solve systems by the substitution method.

To solve using the substitution method:

  1. Isolate or solve for one variable in at least one equation; y = 2x + 3 or x = 4y – 6.
  2. Substitute the expression of the isolated variable into the other equation. Make sure to use parenthesis around the expression if there is a coefficient involved.
  3. Solve the new one-variable equation to get the value of the first variable
  4. Plug that value into one of the original equations and solve for the remaining variable.
  5. Remember to write your values as an ordered pair. (x, y)

Example

 Y = 2x + 10          Y = -2x – 6      The y variable is isolated in BOTH equations.

 2x + 10 = -2x – 6                          Set them equal to each other because y = y

+2x  -10    +2x -10                       Solve as any multi-step equation

       4x  = -16    

         X = -4                                      Substitute the -4 for x in one of the equations and solve for y.

        (-4, 2)                                       Write the values as an ordered pair.

Watch this video to see a few different examples:

Try It

Solve each system by substitution.

  1. y = -3x = 4 and x = 2y + 6
  2. x = 5 and x + y = 8
  3. x = 7 - 2y and 2x + y = 5
  4. At the school store, Ridley bought 2 books and a backpack for a total of $26 before tax.  Each book cost $8 less than the backpack.  Write a system of equations that can be used to solve for the price of each item.  Solve by substitution.   

Click here to see if your solutions are correct. Links to an external site.  

Practice

If you would like to practice more problems and check your work, click here. Links to an external site. Make sure you check your answers and look at the course resources or ask your teacher if there are any problems you do not understand. Links to an external site.

IMAGES CREATED BY GAVS