# System of Equations

### Review & Word Problems

## Tuesday Warm Up

## Monday Warm Up

## 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

## Task 1

## Substitution

## Task 2

## Steps for Substitution

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)

If you need to watch the previous videos on substitution, click this link. Scroll to the bottom and watch the three videos on substitution.

## System Word Problems

## Task 3: Videos

## Task 4: Independent / Whole Group Practice

*Directions: *

- 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)

## Task 5: Group Work

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.

## Task 6: Practice Problems

Be sure to: 1. define your variables 2. set up the system by writing the two equations and 3. solve the system (BE SURE TO SHOW YOUR WORK!).

Last but not least, check your work by plugging in the solution into your two equations.