Solving systems of linear equations by substitution worksheet introduces students to a fundamental technique for solving systems of linear equations. This method involves substituting the value of one variable into another equation to eliminate that variable and solve for the remaining variable.

The worksheet provides a structured approach to understanding and applying the substitution method, making it an invaluable resource for students.

This worksheet is designed to guide students through the substitution method step-by-step, with clear explanations and examples. It also includes practice problems of varying difficulty levels to help students develop their problem-solving skills. Additionally, the worksheet explores real-world applications of solving systems of linear equations, demonstrating the practical significance of this method.

Solving Systems of Linear Equations by Substitution

Systems of linear equations are sets of two or more equations that contain the same variables. Solving these systems is essential in various fields, including mathematics, science, and engineering.

One effective method for solving systems of linear equations is the substitution method. This technique involves isolating one variable in one equation and substituting its expression into the other equation.

This worksheet provides a comprehensive overview of the substitution method, including its steps, examples, practice problems, and applications.

Substitution Method

The substitution method involves the following steps:

1. Solve one equation for one variable in terms of the other variables.
2. Substitute the expression obtained in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value obtained in step 3 back into either of the original equations to find the value of the first variable.

Here’s an example:

Solve the system:

x + y = 5

x- y = 1

Solve the first equation for y:

y = 5- x

Substitute y into the second equation:

x- (5 – x) = 1

2x – 5 = 1

2x = 6

x = 3

Substitute x back into the first equation to find y:

3 + y = 5

y = 2

Therefore, the solution to the system is (x, y) = (3, 2).

Comparison to Other Methods

The substitution method is often compared to other methods for solving systems of linear equations, such as the elimination method.

Here’s a table comparing the two methods:

Method	Steps	Complexity
Substitution	Isolate and substitute	Easier for small systems
Elimination	Add/subtract equations	More efficient for large systems

Worksheet Examples

Here are some examples of systems of equations solved using the substitution method:

System	Solution	Steps
x + y = 10x y = 2	(x, y) = (6, 4)	Substitute y from the first equation into the second equation
2x + 3y = 11x 2y = 1	(x, y) = (3, 2)	Solve the second equation for x and substitute into the first equation

Practice Problems

Here are some practice problems for students to solve using the substitution method:

1. Solve the system: x + y = 7, x
   

   y = 3

2. Solve the system: 2x + y = 5, x
   

   3y = 1

3. Solve the system: 3x
   

   2y = 10, x + y = 5

Answer key:

1. (x, y) = (5, 2)
2. (x, y) = (2, 1)
3. (x, y) = (3, 2)

Applications, Solving systems of linear equations by substitution worksheet

The substitution method is used in various fields, including:

• Physics: Solving problems involving motion, forces, and energy
• Chemistry: Calculating concentrations and equilibrium constants
• Economics: Modeling supply and demand
• Engineering: Designing structures and systems

Answers to Common Questions: Solving Systems Of Linear Equations By Substitution Worksheet

What is the substitution method?

The substitution method is a technique for solving systems of linear equations by substituting the value of one variable into another equation to eliminate that variable.

When should I use the substitution method?

The substitution method is most effective when one of the variables in the system of equations can be easily solved for in terms of the other variable.

What are the steps involved in the substitution method?

The steps involved in the substitution method are:

1. Solve one equation for one variable in terms of the other variable.
2. Substitute the expression from step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value from step 3 back into one of the original equations to solve for the other variable.