Solving a System of Equations Transitively

Solving Systems of Equations

Substitution/Transitive Method ​

Multiple Choice

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

Multiple Choice

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (0, 1)

Multiple Choice

Give the solution to the system.

• (3,1)

• (1,3)

• (-1,3)

• (1, -3)

Multiple Choice

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines

• the same line 

• Intersecting lines

Multiple Choice

• Infinitely Many Solutions

• No Solution

​Learning Target

Today I am learning about solving systems of Equations Algebraically.

Success Criteria

I know that I am successful(proficient) when I can: 

• Solve a System of Equations using the Transitive Method. 

• Determine the type of Solution by examination of the system. 

y = 6x + 10

y = 4x + 6

Step 1: 6x + 10 = 4x + 6

Set the two equations equal to each other.

Step 1:

Steps to Solving a System of Equations - Algebraically

6x + 10 = 4x + 6

-4x -4x

2x + 10 = 6

-10 = -10

2x = -4

2 2

x = -2

Solve for x.

​Step 2:

Steps to Solving a System of Equations - Algebraically

y = 6x + 10

y = 4x + 6

y = 6(-2) + 10

y = -12 + 10

y = -2

Place the value for x in one of the original equations and solve for y.

Step 3:

Solving a System of Equations Algebraically

Solution:

( -2, -2)

Record your solution to the system as an ordered Pair.

Step 4:

Solving a System of Equations Algebraically

Let's Practice!

Multiple Choice

What is the first step in Solving a System of Equations using the Transitive Method?

• Solve for x

• Set the Equations Equal to each other

• Solve for y

• Graph the Equations

Multiple Choice

Which answer choice shows the 1st step in solving a system using the transitive method?

y = x + 1

y = 4x - 7

• x + 1 + 4x = 5

• y = x + 1 + 4x + 5

• x + 1 = 4x + 5

• y = 4x - 5x - 1

Multiple Choice

What is the next step in Solving this System?

y = x + 1

y = 4x - 7

x - 1 = 4x - 7

-x -x

- 1 = 3x - 7

• Add 7 to both sides

• Add 1 to both sides

• add 3x to both sides

• subtract 7 from both sides

Multiple Choice

What is the value of x in this system?

y = x + 1

y = 4x - 7

x - 1 = 4x - 7

-x -x

- 1 = 3x - 7

• x = 8/3

• x = 6

• x = -8

• x = 2

Multiple Choice

What is the value of y in this System of Equations?

y = 2x - 1

y = 6x + 3

2x - 1 = 6x + 3

-2x - 2x

- 1 = 4x + 3

-3 -3

- 4 = 4x

4 = 4

- 1 = x

• y = - 1

• y = 4

• y = -3

• y = 3

Multiple Choice

How do you write an answer to a System of Equations?

• As a fraction

• As an ordered Pair

• As a graph

• In numerical order