Module 1 Lesson 10

In this module you will review systems of linear equations

Module 1 - Lesson 10

Any of the three methods can be used to solve a system of linear equations. The solution is written as (x, y), which represents the point where the two lines intersect. It is the only point they have in common.

Systems of linear equations have three methods for solving: 1. Graphing Method 2. Substitution Method 3. Elimination Method

Lesson 10 - Systems of Linear Equations

Solve:

2x + 3y = 8 y = x + 1

Solution:(1, 2)

Use a graphing calculator or a piece of paper to graph the system of linear functions and find their point of intersection.

Systems of linear equations have three methods for solving: 1. Graphing Method 2. Substitution Method 3. Elimination Method

Lesson 10 - Systems of Linear Equations

y = 1 + 1 y = 2 Solution: (1, 2)

Now substitute the x-value into either equation to get the y-value

2x + 3(x+1) = 8 2x + 3x + 3 = 8 5x + 3 = 8 5x = 5 x = 1

The y variable is already isolated so we can substitute!

Solve. 2x + 3y = 8 y = x+ 1

Using the substitution method, the goal is to isolate one of the variables so you can substitute it into the other equation.

Systems of linear equations have three methods for solving: 1. Graphing Method 2. Substitution Method 3. Elimination Method

Lesson 10 - Systems of Linear Equations

1 2

2x + 3(3) = 8 2x + 9 = 8 2x = -1 x = -

1 2

Solution: (- , 3)

Now, we substitute the y-value into either equation to find the x-value.

5y = 15 y = 3

We have a 2x and -2x, which when combined become zero. Therefore, we can eliminate x.

Solve. 2x + 3y = 8 -2x + 2y = 7

When using the elimination method, the goal is to eliminate one of the variables.

Systems of linear equations have three methods for solving: 1. Graphing Method 2. Substitution Method 3. Elimination Method

Lesson 10 - Systems of Linear Equations

Elimination Method

Graphing Method

Substituion Method

y = −3x + 4 y = 3x − 2

−7x + 4y = 24 4x − 4y = 0

You Try!

3x - y = 233x + y = − 5

2x - 4y = 20y = 3x

You Try!

Algebra 1 Keystone Example Test

Scoring Guidelines for Constructed Response

Keystone Four Function Calculator

Keystone Graphing Calculator

Keystone Formula Sheet

Keystone Resources

Here are resources to help support you through this module and prepare you for the Keystone exam.

Algebra 1 Keystone Example Test

Scoring Guidelines for Constructed Response

Keystone Four Function Calculator

Keystone Graphing Calculator

Keystone Formula Sheet

Keystone Resources

Here are resources to help support you through this module and prepare you for the Keystone exam.

Algebra 1 Keystone Example Test

Scoring Guidelines for Constructed Response

Keystone Four Function Calculator

Keystone Graphing Calculator

Keystone Formula Sheet

Keystone Resources

Here are resources to help support you through this module and prepare you for the Keystone exam.

Algebra 1 Keystone Example Test

Scoring Guidelines for Constructed Response

Keystone Four Function Calculator

Keystone Graphing Calculator

Keystone Formula Sheet

Keystone Resources

Here are resources to help support you through this module and prepare you for the Keystone exam.

Algebra 1 Keystone Example Test

Scoring Guidelines for Constructed Response

Keystone Four Function Calculator

Keystone Graphing Calculator

Keystone Formula Sheet

Keystone Resources

Here are resources to help support you through this module and prepare you for the Keystone exam.

Algebra 1 Keystone Example Test

Scoring Guidelines for Constructed Response

Keystone Four Function Calculator

Keystone Graphing Calculator

Keystone Formula Sheet

Keystone Resources

Here are resources to help support you through this module and prepare you for the Keystone exam.

Algebra 1 Keystone Example Test

Scoring Guidelines for Constructed Response

Keystone Four Function Calculator

Keystone Graphing Calculator

Keystone Formula Sheet

Keystone Resources

Here are resources to help support you through this module and prepare you for the Keystone exam.

Algebra 1 Keystone Example Test

Scoring Guidelines for Constructed Response

Keystone Four Function Calculator

Keystone Graphing Calculator

Keystone Formula Sheet

Keystone Resources

Here are resources to help support you through this module and prepare you for the Keystone exam.