# data[].attributes.body
Graph the two line and find their intersection. That is the answer.

# data[].attributes.body
go to student.desmos. com

Use code 4874Q to access Solutions to Systems of Equations

Use code SHZZP to access
Playing Catch-Up

# data[].attributes.body
3 examples of substitution.
2 work and one doen't

# data[].attributes.attachment_link.readable_text
The substitution method is one of two ways to solve systems of equations without graphing.

You might ask yourself, "Why wouldn't I just want to graph the equations to find the solution?" Well there are many reasons...

You may not have graph paper or an accurate way to graph the equations, thus making it hard to identify the solution.

Or, as the equations become more difficult, the solution is not always an identifiable point on the graph. This means that the solution may contain decimals or fractions, which is not easy to identify on a graph.

Once you learn the algebraic method for solving a system of equations, you will probably find that it becomes your preferred method. Graphing becomes too tedious.

The good news is that there are two methods, which makes this process easier depending on the problems you are given.

So, let's get to it!

The following steps can be used as a guide as you read through the examples for using the substitution method.

Steps for Using the Substitution Method in order to Solve Systems of Equations

Solve 1 equation for 1 variable. (Put in y = or x = form)

Substitute this expression into the other equation and solve for the missing variable.

Substitute your answer into the first equation and solve.

Check the solution.

These directions will make a lot more sense when you study the examples below.

Example 1

The next example demonstrates a situation where it is easier to solve for x initially.

Example 2

Let's take a look at another example. You'll find this very interesting! Pay close attention to the very last step of the solution.

Example 3

Ok... one more unique example. Again, pay attention to the end result.

Example 4

Need Help With Your Homework?

Try this calculator for step by step answers (with subscription)

Take a look at the questions that other students have submitted:

Other Lessons You Might Like on Systems of Equations
Top of the Page

# data[].attributes.attachment_link.description
The substitution method is one of two ways to solve systems of equations without graphing. You might ask yourself, "Why wouldn't I just want to graph the equations to find the solution?" Well there are many reasons... You may not have graph paper or an accurate way to graph the equations, thus making it hard to identify the solution.

# data[].attributes.body
It is a little trickier when one pair of values are not equal and opposite. However, they can be made that way with multiplication.

# data[].attributes.body
Begin with graphing the line as if it were an equality then using points from both sides of line but not on the line test to for which side to shade.

# data[].attributes.headline
Why is one line solid and the other dotted?

# data[].attributes.subject
Why is one line solid and the other dotted?

# data[].attributes.headline
Making the Most or Least, of Linear Inequalities

# data[].attributes.subject
Making the Most or Least, of Linear Inequalities

# data[].attributes.body
This site has a real-world application for you to try.

# data[].attributes.attachment_link.title
Making the Most, or the Least, of Linear Inequalities | Learn It Part 1

# data[].attributes.attachment_link.description
Hermione is starting her own business, Cupcakes and Cake-Ups Bakery. She and her staff can make at most 800 cupcakes and 600 cakes in one day. Her current bakery is small and therefore can hold 1,000 cupcakes and cakes altogether.

# data[].attributes.headline
Graph of a systems of linear inequalities

# data[].attributes.subject
Graph of a systems of linear inequalities

# data[].attributes.body
Notice that the solution is now a region and not just one point. It is where the shading overlaps.

# data[].attributes.body
go to student.desmos. com

Use code 4874Q to access Solutions to Systems of Equations

Use code SHZZP to access
Playing Catch-Up

# data[].attributes.body
go to student.desmos.com

Use code RV6VG to access
Card Sort: Linear Equations

# data[].attributes.body
Short video

# data[].attributes.attachment_link.title
Solving Systems of Equations - MathHelp.com - Algebra Help

# data[].attributes.attachment_link.description
For a complete lesson on solving systems of equations, go to http://www.MathHelp.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve a system of linear equations by addition.

# data[].attributes.headline
Solving Systems of Equations by Graphing by Shmoop

# data[].attributes.subject
Solving Systems of Equations by Graphing by Shmoop

# data[].attributes.attachment_link.title
Solving Systems of Equations by Graphing by Shmoop

# data[].attributes.attachment_link.description
To solve systems of equations by graphing simplify the equations to be in slope intercept form (y=mx+b) and then graph them. Finally, find the intersection point and you have your variable values. Solving Systems of Equations by Graphing: http://www.shmoop.com/linear-equation-systems/graphing-linear-equation-systems.html

# data[].attributes.headline
Introduction to Systems of Equations by Shmoop

# data[].attributes.subject
Introduction to Systems of Equations by Shmoop

# data[].attributes.attachment_link.title
Introduction to Systems of Equations by Shmoop

# data[].attributes.attachment_link.description
Here's a general overview of systems of equations, those pesky equations with a ton of variables. For more Shmoop and more math, visit our website at: http://www.shmoop.com/learning-guides/

# data[].attributes.headline
Solving Systems of Equations using Substitution - Concept

# data[].attributes.subject
Solving Systems of Equations using Substitution - Concept

# data[].attributes.attachment_link.title
Solving Systems of Equations using Substitution - Concept - Algebra Video by Brightstorm

# data[].attributes.attachment_link.description
Video explanation on how to solve systems of equations by substitution. Time-saving online video on solving systems of equations by substitution and example problems. Concept explanation.

# data[].attributes.headline
Solving Systems of Equations by Substitution by Shmoop

# data[].attributes.subject
Solving Systems of Equations by Substitution by Shmoop

# data[].attributes.attachment_link.title
Solving Systems of Equations by Substitution by Shmoop

# data[].attributes.headline
Solving systems of equations tutorial with substitution

# data[].attributes.subject
Solving systems of equations tutorial with substitution

# data[].attributes.attachment_link.title
Solving systems of equations tutorial with substitution

# data[].attributes.attachment_link.description
Learn how to solve a system of equations by substitution. To solve a system of equations means to obtain a common value of the variables that makes the each of the equation in the system true.

# data[].attributes.attachment_link.title
How Do You Use a System of Linear Equations to Find Coordinates on a Map? | Virtual Nerd

# data[].attributes.attachment_link.description
Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.