Systems of Equations: Graphing

Systems of Equations: Graphing

Open Ended

Do you have any good things to share? If so, what is your good thing? [Mine is that I got my new glasses yesterday!]

Poll

How are you feeling today?

• Happy

• Sad

• Mad

• Tired

Poll

This week, I've mainly been...

• happy.

• sad.

• lonely.

• frustrated.

Poll

The color that makes me smile MOST is...

• Blue

• Yellow

• Orange

• Pink

• Purple

Multiple Choice

Solve the following

y = - 8

y = 6x + 10

• No Solution

• (-3,-8)

• y = - 8

• x = - 3

Multiple Choice

Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-3,-8)
• (-8,-3)
• (3,-8)
• (8,3)

Different types of solutions

1. One solution: The solution is where the points intersect

2. No solution: The lines will never intersect so this system does not have an answer

3. Infinite solutions: The lines have the same equation.

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

How many solutions will this system have?

• one solution

• no solution

• infinitely many solutions

Multiple Choice

Parallel Lines never intersect because...

• they have the same slopes. 
• they have the same y-intercept.
• they have different slopes.
• they have different y-intercepts. 

Multiple Choice

What is the solution to the system?

• (3, -1)
• (2, -6)
• No Solution 
• (6, -2)

Multiple Choice

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (0, 1)

Multiple Choice

How many solutions does this system of equations have?

• One Solution
• No solution
• Infinitely Many Solutions
• Two Solutions

Multiple Choice

What is the solution?

• (6, 3)
• (3, 6)
• (-6, 3)
• No solution

Multiple Choice

The solution is:

• (4, 3)
• (3, 4)
• (-4, 3)
• No solution

Multiple Choice

What is the solution?

• No solution
• (0, 2)
• (0, -4)
• (3, -3)

Multiple Choice

Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-1, 4)
• (1, -4)
• (-4, 1)
• (4, -1)

Multiple Choice

What is the solution?

• (6, 3)
• (3, 6)
• (-6, 3)
• No solution

Multiple Choice

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat.  Write an equation for C, the total cost, to rent the boat for h hours.

• h = 2C + 15
• C = 15h + 2
• h = 15C + 2
• C = 2h + 15

Multiple Choice

^{What is the solution?}

• 1

• -2

• (1, 2)

• (1, -1)

Multiple Choice

This system has _____ solutions

• no
• 1
• 2
• Infinitely many

Multiple Choice

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines
• Same line
• Parallel lines

Multiple Choice

These two lines intersect at _____.

• (4, -2)
• (4, 2)
• (-2, 4) 
• No solution

Multiple Choice

The solution to this system of equations is:

• (4, 3)
• (3, 4)
• (-4, 3)
• No solution

Multiple Choice

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (2, 0)