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

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:

3

x+ 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

Solving Using Substitution Method through a series of mathematical
steps to teach students algebra

2*x* + 5*y* = 6

9*y* + 2*x* =22

The following video shows another example of of
solving systems of equations by substitution.

*y* = 2*x* + 5 *
*3

This video explains the steps to solve a linear system of equations
using the substitution method.

*x* + 3*y* = 12

2*x* + *y* = 6

The following is an example of a system of equations that is solved
using the substitution method.

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

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

This video provides an example of how to solve a system of linear
equation using the substitution method.

*x +* 2

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.