# 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
x=-4y

Stacey D.

### Comments for Systems of Equations Substitution Method

Average Rating     Apr 24, 2010 Rating     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: https://www.algebra-class.com/substitution-method.html Best of luck, Karin Need More Help With Your Algebra Studies?