# Solving Systems of Equations by Substitution

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:

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 2 and isolate variable y
y = 3x - 8         (equation 3)

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

We can then substitute the variable y in equation 1 with 3x - 8
3x + 2(3x - 8) = 2

3x + 6x - 16 = 2

9x - 16 = 2

Step 5: Isolate variable x

9x = 18

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

y = 3(2) - 8
y = 6 - 8 = -2

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

Answer: x = 2 and y = -2

Solving systems of equations using Substitution Method through a series of mathematical steps to teach students algebra
Example:
2x + 5y = 6
9y + 2x = 22 How to solve systems of equations by substitution?
Example:
y = 2x + 5
3x - 2y = -9 Steps to solve a linear system of equations using the substitution method
Example:
x + 3y = 12
2x + y = 6 Example of a system of equations that is solved using the substitution method.
Example:
2x + 3y = 13
-2x + y = -9

Solving Linear Systems of Equations Using Substitution
Include an explanation of the graphs - one solution, no solution, infinite solutions
Examples: 2x + 4y = 4
y = x - 2

x + 3y = 6
2x + 6y = -12

2x - 3y = 6
4x - 6y = 12 Example of how to solve a system of linear equation using the substitution method.
x + 2y = -20
y = 2x

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