# System of Equations

## System of Equations

There are three ways to solve a system: graphing, substitution method, and elimination method. This year we will learn two out of the three methods: graphing and substitution. Next year in Math I, you will learn the elimination method.

There are three types of solutions:
1. One solution - when two lines intersect, they cross at one point. That point is the solution to the system.

2. No solution - when two lines are parallel, meaning they have the same slope, they will never intersect meaning there is no solution.

3. Infinite solutions - when the two lines have the same equation, they will always intersect which means there are infinite solutions. That means that no matter what value you plug in for x, the y values will always be the same.

## Graphing Systems

Watch the video on graphing practice to refresh your memory. Then practice graphing by clicking on the link below.
Solving Systems by Graphing - MathHelp.com - Algebra Help

## Substitution

Watch the video on substitution. Then work on the matching activity that follows for practice. (On a separate sheet of paper) Match each system with its correct solution. When finished, ask for me to come check your paper.
Review of Systems of Equations: Lesson 054

## Steps for Substitution

1. Change one of the equations into slope intercept form.

2. Substitute the slope intercept form equation into the standard for equation.

3. Solve for x.

4. Substitute x into the equation in slope intercept form.

5. Solve for y.

6. Write the equation as an ordered pair. (x, y)

## Substitution Matching Activity

Directions: Solve each system by substitution and then match the system to the solution. You will use each solution only once.

1. 2x + 3y = 5
x = 5y + 9

2. 3x + 2y = 6

y = -2x + 2

3. x = -3y – 2

-4x – 5y = 8

4. x = -4

2x + y = -10

5. x = 2y – 3

4x – 5y = -3

6. –x + y = -17

3x + y = -17

7. -6x + 2y = -14

5x = 2y + 12

8. 2y + x = 2

7x – 3y = -20

9. 3x + 2y = 10

y = 2x - 9

10. x + 2y = 2

4y = -3x – 4

A. (3, 3)

B. (0, -17)

C. (4, -1)

D. (-2, 6)

E. (2, -1)

F. (-4, -2)

G. (-2, 0)

H. (-8, 5)

I. (-2, 2)

J. (4, -1)

## System Word Problems

Watch the three videos to introduce you to how to solve system word problems.

## Task 4: Independent / Whole Group Practice

Directions:

Set up each system by writing two linear equations.
- Be sure to assign a variable to each item described in the problem.

Solve the word problem by using the substitution method.

Write you solution as an ordered pair. (x, y)

I will assign you and your group a specific problem to solve and explain. On the big white boards, please set up the system of equation from the problem and then find the solution. Work together with your group and make sure everyone in your group is able to explain how to set up and solve the problem.
Following the activity, we will have groups share their work with the class. Someone will read the problem to the group, someone will explain how to set up the system, and someone else will explain how to solve the system in order to find the solution, an (x, y) pair.