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

Thank you for your help
Stacey D.

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Apr 24, 2010
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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

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