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Worksheets to practice solving systems of equations

More Algebra Lessons

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

y + 8 = 3x (equation 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

Worksheets to practice solving systems of equations

More Algebra Lessons

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.

The following example show the steps to solve a system of equations using the substitution method. Scroll down the page for more examples and solutions.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.

**Steps to solving Systems of Equations by Substitution:**

1. Isolate a variable in one of the equations. (Either y = or x =).

2. Substitute the isolated variable in the other equation.

3. This will result in an equation with one variable. Solve the equation.

4. Substitute the solution from step 3 into another equation to solve for the other variable.

5. Recommended: Check the solution.

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

Step 3: Remove brackets using distributive property

3x + 6x - 16 = 2

Step 4: Combine like terms

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

Step 7: Check your answer with equation 1

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

Answer: x = 2 and y = -2

Example:

2x + 5y = 6

9y + 2x = 22

Example:

y = 2x + 5

3x - 2y = -9

Example:

x + 3y = 12

2x + y = 6

Example:

2x + 3y = 13

-2x + y = -9

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

x + 2y = -20

y = 2x

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