Module 1 Lesson 10

Module 1 - Lesson 10

In this module you will review systems of linear equations

Lesson 10 - Systems of Linear Equations

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

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

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

Solve:

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

Solution:(1, 2)

Lesson 10 - Systems of Linear Equations

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

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

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!

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

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

Lesson 10 - Systems of Linear Equations

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

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

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

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

5y = 15 y = 3

1 2

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

1 2

Solution: (- , 3)

Elimination Method

Substituion Method

Graphing Method

You Try!

y = −3x + 4 y = 3x − 2

−7x + 4y = 24 4x − 4y = 0

You Try!

3x - y = 233x + y = − 5

2x - 4y = 20y = 3x

Keystone Resources

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

Keystone Formula Sheet

Keystone Graphing Calculator

Keystone Four Function Calculator

Scoring Guidelines for Constructed Response

Algebra 1 Keystone Example Test

Keystone Resources

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

Keystone Formula Sheet

Keystone Graphing Calculator

Keystone Four Function Calculator

Scoring Guidelines for Constructed Response

Algebra 1 Keystone Example Test

Keystone Resources

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

Keystone Formula Sheet

Keystone Graphing Calculator

Keystone Four Function Calculator

Scoring Guidelines for Constructed Response

Algebra 1 Keystone Example Test

Keystone Resources

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

Keystone Formula Sheet

Keystone Graphing Calculator

Keystone Four Function Calculator

Scoring Guidelines for Constructed Response

Algebra 1 Keystone Example Test

Keystone Resources

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

Keystone Formula Sheet

Keystone Graphing Calculator

Keystone Four Function Calculator

Scoring Guidelines for Constructed Response

Algebra 1 Keystone Example Test

Keystone Resources

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

Keystone Formula Sheet

Keystone Graphing Calculator

Keystone Four Function Calculator

Scoring Guidelines for Constructed Response

Algebra 1 Keystone Example Test

Keystone Resources

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

Keystone Formula Sheet

Keystone Graphing Calculator

Keystone Four Function Calculator

Scoring Guidelines for Constructed Response

Algebra 1 Keystone Example Test

Keystone Resources

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

Keystone Formula Sheet

Keystone Graphing Calculator

Keystone Four Function Calculator

Scoring Guidelines for Constructed Response

Algebra 1 Keystone Example Test