These algebra lessons introduce the technique of solving systems of
equations by substitution.

**Solving systems of equations using Substitution Method through a series of mathematical
steps to teach students algebra**

Example:

2*x* + 5*y* = 6

9*y* + 2*x* = 22
**How to solve systems of equations by substitution?**

Example:

*y* = 2*x* + 5

3*x* - 2*y* = -9
**Steps to solve a linear system of equations
using the substitution method**

Example:

*x* + 3*y* = 12

2*x* + *y* = 6
**Example of a system of equations that is solved
using the substitution method.**

Example:

2*x* + 3*y* = 13

-2*x* + *y* = -9

**Solving Linear Systems of Equations Using Substitution**

Include an explanation of the graphs - one solution, no solution, infinite solutions

Examples: 2*x* + 4*y* = 4

*y* = *x* - 2

*x* + 3*y* = 6

2*x* + 6*y* = -12

2*x* - 3*y* = 6

4*x* - 6*y* = 12
**Example of how to solve a system of linear
equation using the substitution method.**

*x* + 2*y* = -20

*y* = 2*x*

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

In some word problems, we may need to translate the sentences
into more than one equation.
If we have two unknown variables then we would need at least two
equations to solve the variable. In general, if we have *n *unknown
variables then we would need at least *n *equations to
solve the variable.

In the Substitution Method, we isolate
one of the variables
in one of the equations and substitute the results in the other
equation. We usually try to choose the equation where the coefficient
of a variable is 1 and isolate that variable. This is to avoid
dealing with fractions whenever possible. If none of the variables
has a coefficient of 1 then you may want to consider the Addition
Method or Elimination Method.

Related Topics:

Worksheets to practice solving systems of
equations

More
Algebra Lessons

Example:

3x+ 2y= 2(equation 1)

y+ 8 = 3x (equation 2)

Solution:

Step 1: Try to choose the equation where the coefficient of a variable is 1.

Choose

equation 2and isolate variabley

y= 3x- 8(equation 3)

Step 2: From *
equation 3*, we know that *y* is the same as 3*x* - 8

We can then substitute the variable

yinequation 1with 3x- 8

3x+ 2(3x- 8) = 2

Step 3: Remove brackets using distributive property

3

x+ 6x- 16 = 2

Step 4: Combine like terms

9

x- 16 = 2

Step 5: Isolate
variable *x *

9

x= 18

Step 6: Substitute *x*
= 2 into * equation 3* to get the
value for *y *

y= 3(2) - 8

y= 6 - 8 = -2

Step 7: Check your answer
with *equation 1*

3(2) + 2(-2) = 6 - 4 = 2

Answer:* x* = 2
and *y* = -2

Example:

2

9

Example:

3

Example:

2

Example:

2

-2

Include an explanation of the graphs - one solution, no solution, infinite solutions

Examples: 2

2

2

4

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.