Algebra and Pre-Algebra Lessons

Algebra 1 | Pre-Algebra | Practice Tests | Algebra Readiness Test

Algebra E-Course and Homework Information

Algebra E-course Info | Log In to Algebra E-course | Homework Calculator

Formulas and Cheat Sheets

Formulas | Algebra Cheat Sheets

Systems of Equations Substitution Method

Hello, Here I am back in school after 22 years. Math is one of my requirements, before graduation in 2011. However, I am having difficulty understanding this method.

My beginning process of which is the "lonely" factor and substitution. Could you help me please? I have an example my professor gave, but great difficulties; ex. x-y=5

Thank you for your help
Stacey D.

Comments for Systems of Equations Substitution Method

Average Rating starstarstarstarstar

Click here to add your own comments

Apr 24, 2010
Systems of Equations Substitution Method
by: Karin

Hi Stacey,

The substitution method is used quite frequently when solving systems of equations.

As the name dictates, we will be substituting one equation into the other. Let's take a look at your two equations.

x - y = 5
x = -4y

Take a look at equation #2 (x = -4y). Since we know that x is equal to -4y, we can substitute -4y for x in the 1st equation.

x - y = 5
-4y - y = 5 (Notice how I replaced x with -4y)

Now we just simplify and solve.

-4y - y = 5
-5y = 5 Combine like terms.
-5y/-5 = 5/-5 Divide both sides by -5

y = -1 The y coordinate of the solution is -1

Now we need to find the x coordinate. We will substitute -1 for y into the equation, x = -4y.

x = -4y
x = -4(-1) I substituted -1 for y.
x = 4 The x coordinate is 4

The solution to this system of equations is
(4, -1).

This is a solution to both equations and it is the point where the two lines would intersect on a graph.

I hope this helps! If you need more examples, please go to: http://www.algebra-class.com/substitution-method.html

Best of luck,

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Students.

Like This Page?

Top of the Page

Connect and Follow Algebra Class

Copyright © 2009-2015 Karin Hutchinson ALL RIGHTS RESERVED